I'll go with the dog

Pokemon: Lucario
Type: Fighting/Steel
Ability:
=Steadfast (Increases Speed by 1.5x when Flinched)
=Inner Focus (Prevents flinching except from Focus Punch)
Base Stats:
=HP: 70
=Attack: 110
=Defense: 70
=Special Attack: 115
=Special Defense: 70
=Speed: 90
=Total: 525
Weakness (2x): Fighting, Ground, & Fire
Resistance (.5x): Normal, Ghost, Steel, Grass, Ice, & Dragon
Resistance (.25x) Rock, Bug, & Dark
Immunity (0x): Poison
Moveset Analysis (Level Up):
Now I see the Ground-type Bone Rush which can handle its Fire-type weakness. From there it can learn the Dark-type Dark Pulse; Dragon-type Dragon Pulse; Normal-type Quick Attack, Feint, and ExtremeSpeed; Steel-type Metal Claw (STAB); and Fighting-type Counter, Force Palm, Aura Sphere, and Close Combat (STAB). For tactical use it has Foresight, Detect, Metal Sound, and Sword Dance.
Moveset Analysis (TM/HM):
Water-type Water Pulse further handles Fire-types as well as Ground-types, and you can even do a Rain Dance previous to that to increase Water Pulse's power. I also see a nice Psychic-type Psychic to handle other Fighting-types that want to get in the ring. As if you didn't have enough counters for Fire-types, there are also the Rock-types Stone Edge and Rock Slide as well as Ground-types Earthquake and Dig. Other moves are Normal-type Hyper Beam, Strength, and Rock Climb; Ghost-type Shadow Ball; Dark-type Payback; Poison-type Poison Jab; Steel-type Iron Tail and Flahs Cannon (STAB); and Fighting-type Focus Punch, Brick Break, Focus Blast, and Drain Punch (STAB). Want to further increase Lucario's stats you can also use Calm Mind and/or Bulk Up.
Moveset Analysis (Breeding):
The main focus here are the Fighting-type Cross Chop, Hi Jump Kick, Low Kick, and Sky Uppercut (STAB). Other useful moves might be Dark-type Bite and Crunch and Fire-type Blaze Kick.
Moveset Analysis (Tutoring):
We've got two of the Elemental Punches, Ice-type Ice Punch and Electric-type ThunderPunch, and with Ice Punch handling Ground-types that's really good (but why no Fire Punch?). Only true worth wild thing here is Psychic-type Zen Heabdutt to further handle Fighting-types, but that's it. I do see Magnet Rise though that can protect it from those hurtful Ground-type attacks though.

Pokemon: Steelix
Type: Steel/Ground
Ability:
=Rock Head (Prevents recoil damage except from a Life Orb or using Struggle)
=Sturdy (Prevents OHKO moves)
Base Stats:
=HP: 75
=Attack: 85
=Defense: 200
=Special Attack: 55
=Special Defense: 65
=Speed: 30
=Total: 510
Weakness (2x): Fighting, Ground, Fire, & Water
Resistance (.5x): Normal, Flying, Bug, Ghost, Steel, Psychic, Dragon, & Dark
Resistance (.25x) Rock
Immunity (0x): Poison & Electric
Moveset Analysis (Level Up):
I see Elemental Fangs! Which is good, as Electric-type Thunder Fang handles Water-types and Ice-type Ice Fang handles Ground-types. That Fire-type weakness is handle the the truck load of Rock-type moves Rock Throw, Rock Tomb, and Stone Edge. There is also Dragon-type DragonBreath; Dark-type Crunch; Normal-type Slam; and Steel-type Iron Tail (STAB). Surprisingly no Ground-type attack moves. There is also Rock Polish if you want to be faster or Curse to give up Speed and gain more Attack and Defense.
Moveset Analysis (TM/HM):
Since there was no Ground-type moves listed above, I'll list them first. Ground-types Earthquake and Dig (STAB) and while we're at it Steel-type Flash Cannon and Gyro Ball (STAB). Normal-type Hyper Beam, Strength, and Rock Climb; Rock-type Rock slide; Dark-type Payback and Dark Pulse; and Dragon-type Dragon Pulse. Sandstorm and Stealth Rock might also be useful here.
Moveset Analysis (Breeding):
We got the Normal-type Explosion and the Rock-type Rock Blast. But what steels the show here is the combo Defense Curl and Rock-type Rollout (and if you face Whitney and her Miltank you'll know how evil this combo is).
Moveset Analysis (Tutoring):
Water-type Aqua Tail; Rock-type Ancient Power; Dragon-type Twister; Ground-type Earth Power (STAB); and Steel-type Iron Head (STAB). It too also has Magnet Rise to make Ground-type attacks not effective against it.

I'm sorry, but Lucario will be running circles around Steelix. And when it's done doing that, it can take adventage of its high Special Attack and Steelix's low Special Defense and blast it away with a STAB Aura Sphere or Focus Blast. And even if it could stand it, Lucario could probably take one of Steelix's attacks anyway meaning if Lucario doesn't take it down first turn, it'll do the next turn.

MY CHOICE:
LUCARIO


Lucario: 3 | Steelix: 1

Beauty or power?

I'll pick later

Pokemon: Gyarados
Type: Water/Flying
Ability: Intimidate
=(In Battle: Lowers opponent's Attack by one stage when entering into battle)
=(Outside Battle: If leading the party, chances of encountering a low level wild Pokemon decreases by 50%)
Base Stats:
=HP: 95
=Attack: 125
=Defense: 79
=Special Attack: 60
=Special Defense: 100
=Speed: 81
=Total: 540
Weakness (4x): Electric
Weakness (2x): Rock
Resistance (.5x): Fighting, Bug, Steel, Fire, & Water
Immunity (0x): Ground
Moveset Analysis (Level Up):
Rock-type weakness is prett much handled by its Water-type Aqua Tail and Hydro Pump (STAB too!). It can also leanr Normal-type Thrash and Hyper Beam, Dark-type Bite; Dragon-type Dragon Rage (though doesn't really matter) and Twister; and finally Ice-type Ice Fang. As for tactical moves, there is Rain Dance they'll increase Water-type attacks.
Moveset Analysis (TM/HM):
Got some Electric-types you need to get rid of? Ground-type Earthquake will take care of them! There is a ide range of types here. Water-type Water Pulse, Brine, Surf, & Waterfall (STAB); Ice-type Ice Beam, Blizzard, & Avalanche; Electric-type Thunberbolt & Thunder; Fire-type Flamethrower & Fire Blast; Rock-type Stone Edge; Dark-type Payback & Dark Pulse; Normal-type Giga Impact; and Dragon-type Dragon Pulse. We additionally can do a Rain Dance + Thunder and/or Hail + Blizzard combo.
Moveset Analysis (Breeding):
None. It can't learn any moves from breeding, possibly because Magikarp is suppose to be useless and a strong move through breeding will defeat the purpose of that.
Moveset Analysis (Tutoring):
Water-type Aqua Tail & Dive is here (STAD), and it's only Flying-type move Bounce is also here (STAB). There is also Ice-type Icy Wind; Dragon-type Outrage; and Steel-type Iron Head. Spite is also here if you want to wittle down your opponent's PP.

Pokemon: Milotic
Type: Water
Ability: Marcel Scale (Defense is raised when afflicted by a status condition)
Base Stats:
=HP: 95
=Attack: 60
=Defense: 79
=Special Attack: 100
=Special Defense: 125
=Speed: 81
=Total: 540
Weakness (2x): Grass & Electric
Resistance (.5x): Steel, Fire, Water, & Ice
Moveset Analysis (Level Up):
Nothing to handle weaknesses so let's handle its STAB moves. Water-type Water Pulse, Aqua Tail, & Hydro Pump (STAB). Only other noticeable attacks is Dragon-type Twister. Tactical we have Aqua Ring to heal HP, Refresh to heal most status conditions, Recover to one turn complete heal, Rain Dance to power Water-type moves, Safeguard to prevent status conditions, and finally Attract.
Moveset Analysis (TM/HM):
To handle Grass-types, there is Ice-type Ice Beam, Blizzard, and Avalanche. Other moves include Water-type Surf and Waterfall (STAB); Dragon-type Dragon Pulse; and Normal-type Giga Impact and Hyper Beam; and Steel-type Iron Tail. And as I said, the combo Hail + Blizzard will make things a lot easier to handle that Grass-type weakness.
Moveset Analysis (Breeding):
Besides Dragont-type Dragon Pulse, there is only status moves. Confuse Ray for confusion, Hypnosis to induce sleep, Haze to clear stat changes, Mist to protect you from stat changes, Light Screen halves Special Attack damage, Mirror Caot sends back Special Attack damage at twice the power, and Mud Sport to power down Electric-type attacks.
Moveset Analysis (Tutoring):
We now have a move to handle Electric-types, but Ground-type Mud-Slap isn't really that strong to begin with. And besides that there is Water-type Dice (STAB); Ice-type Icy Wind; and Steal-type Iron Head.

Nothing to weaken Gyarados with while Gyarados has some nice Electric-type attacks which Milotic might survive for one turn but not the next. So this battle goes to Gyarados, Milotic should really stay to Pokemon Contests.

MY CHOICE:
GYARADOS

Gyarados: 2 | Milotic: 0

I was going to wait for someone to pick so that I can pick the next clash

gyarados

hey pika how do you put pics?

Pokemon: Gengar
Type: Ghost/Poison
Ability: Levitate (Gives immunity to Ground-types and is unaffected by Arena Trap)
Base Stats:
=HP: 60
=Attack: 65
=Defense: 60
=Special Attack: 130
=Special Defense: 75
=Speed: 110
=Total: 500
Weakness (2x): Ghost, Psychic, & Dark
Resistance (.5x): Grass
Resistance (.25x): Poison & Bug
Immunity (0x): Normal, Fighting, & Ground
Moveset Analysis (Level Up):
Interesting that it's weak to Ghost, Psychic, & Dark and those are the only type of damaging moves it knows. To handle it's Ghost- and Psychic-type weaknesses we have the Dark-type Sucker Punch, Payback, and Dark Pulse; and we also have Ghost-type Nightshade, Shadow Punch and Shadow Ball (STAB). Nothing to handle Dark-types so we'll move on. On the tactical side we have Hypnosis, Spite, Mean Look, Confuse Ray, and Destiny Bond. We also have Curse which I'm sure we all know what that means with a Ghost-type. And stemming off from Hypnosis we can combo it with the Psychic-type Dream Eater and/or the move Nightmare.
Moveset Analysis (TM/HM):
Now what to do about those darn Dark-types... I know! How about Fighting-type Focus Punch, Brick Break, Focus Blast, and Drain Punch! For other types we got Psychic-type Psychic; Grass-type Giga Drain & Energy Ball; Electric-type Thunderbolt & Thunder; Normal-type Hyper Beam, Explosion, Giga Impact & Strength; Ghost-type Shadow Claw (STAB); and Poison-type Sludge Bomb & Poison Jab (STAB). In combos we have Rain Dance + Thunder. Finally I'll like to note we also have Will-O-Wisp.
Moveset Analysis (Breeding):
Elemental punches! Got Fire-type Fire Punch, Ice-type Ice Punch, and Electric-type Thunder Punch. We also have Psychic-type Psywave and Ghost-type Astonish (STAB). Tactical we have Disable, Haze, Perish Song, & Grudge.
Moveset Analysis (Tutoring):
Elemental punche... wait, I already mentioned that. Here we have the Ice-type Icy Wind and Ghost-type Ominous Wind (STAB). Finally we have Pain SPlit and Magic Coat for anything left that is interesting.

Pokemon: Umbreon
Type: Dark
Ability: Synchronize
=(In Battle: Inflicts the opponent with the same status condition if just inflicted)
=(Outside Battle: Increases the chance of enountering a wild Pokemon of the same nature)
Base Stats:
=HP: 95
=Attack: 65
=Defense: 110
=Special Attack: 60
=Special Defense: 130
=Speed: 65
=Total: 525
Weakness (2x): Fighting & Bug
Resistance (.5x): Ghost & Dark
Immunity (0x): Psychic
Moveset Analysis (Level Up):
Nothing to handle weaknesses just yet so moving on. We have Dark-type Pursuit, Faint Attack, and Assurance (STAB); and Normal-type Tackle, Quick Attack, and Last Resort. In tactical we have Confuse Ray, Mean Look, and Moonlight.
Moveset Analysis (TM/HM):
Pyschic-type Psychic and Dream Eater can handle the Fighting-type weakness. We have Ground-type Dig; Steel-type Iron Tail; Ghost-type Shadow Ball; Normal-type Hyper Beam, & Giga Impact; and Dark-type Payback & Dark Pulse (STAB). Sunny Day also is useful as it makes Moonlight heal 2/3 max HP (odd, but true).
Moveset Analysis (Breeding):
We have Normal-type Flail for an attack. There is also Curse, Detect, Wish, and Yawn (to use Dream Eater you got to put the opponent to sleep somehow).
Moveset Analysis (Tutoring):
Dark-type Sucker Punch (STAB) and Normal-type Swift. Other things to mention would be Heal Bell and Spite.

I've got to say, I don't know which one will win as they are pretty much even. Gengar has speed and Fighting-type attacks, but Umbreon got its offensive power and at least one attack in each type Gengar is weak in. It all comes down to tactics really and Gengar has that hands down, if only for Hypnosis.

MY CHOICE:
GENGAR

Gengar: 3 | Umbreon: 0

gliscor vs. scizor?

oh haha veeeerrry funny....

Gliscor

Pokemon: Scizor
Type: Bug/Steel
Ability:
= Swarm
+ (In Battle: Raises Bug-type moves by 150% if HP is below 1/3)
+ (Outside Battle: If leading the party, chances of encountering wild Pokemon increase)
= Technician (Move with power 60 or less get increased by 1.5x)
Base Stats:
=HP: 70
=Attack: 130
=Defense: 100
=Special Attack: 55
=Special Defense: 80
=Speed: 65
=Total: 500
Weakness (4x): Fire
Resistance (.5x): Normal, Bug, Ghost, Steel, Psychic, Ice, Dragon, & Dark
Resistance (.25x): Grass
Immunity (0x): Poison
Moveset Analysis (Level Up):
Nothing to handle its weakness so we'll move on. Dark-type Pursuit & Nightslash; Normal-type Flase Swipe, Slash, Razor Wind, Double Hit, & Feint; Steel-type Bullet Punch & Iron Head (STAB); and Bug-type Fury Cutter & X-Scissor (STAB). The tactical side is mostly moves which increase its own stats such as Swords Dance, Iron Defense, Agility, and Focus Energy.
Moveset Analysis (TM/HM):
Nothing for its weakness again. Normal-type Hyper Beam, Giga Impact, & Strength; Fighting-type Brick Break; Flying-type Aerial Ace; Steel-type Steel Wing & Flash Cannon (STAB); and Bug-type Silver Wind & U-turn (STAB). Tactical we have Sandstorm which doesn't hurt Steel-types and Roost for healing.
Moveset Analysis (Breeding):
Nothing for weakness, going on. Fighting-type Counter & Reversal; and Bug-type Bug Buzz (STAB). Other tactical moves are Light Screen, Safeguard, and Baton Pass if you want to give on those stats increase Scizor's tactical side specailizes in.
Moveset Analysis (Tutoring):
And as a final nail in the coffin, no weakness counter here meaning it might be a good idea to pull out if you come against a Fire-type. Ghost-type Ominous Wind; Normal-type Swift; and Fighting-type Superpower are the only thing I think is worth mentioning.

Pokemon: Gliscor
Type: Ground/Flying
Ability:
= Hyper Cutter (Prevents the Attack stat from being reduced)
= Sand Veil
+ (In Battle: Evasion incrases by 25% in a Sandstorm and doesn't get hurt in a Sandstorm)
+ (Outside of Battle: If this Pokemon is leading your party and are in an area with a sandstorm, the wild Pokemon encounter rate is decreased by 50%)
Base Stats:
=HP: 75
=Attack: 95
=Defense: 125
=Special Attack: 45
=Special Defense: 75
=Speed: 95
=Total: 510
Weakness (4x): Ice
Weakness (2x): Water
Resistance (.5x): Fighting, Poison, & Bug
Immunity (0x): Ground & Electric
Moveset Analysis (Level Up):
And right here we just handled all of the weaknesses. Why? ELEMENTAL FANGS! Fire-type Fire Fang handles Ice-types and Electric-type Thunder Fang handles Water-types, and you still have Ice-type Ice Fang as a nice leftover. We also have Poison-type Poison Jab; Darj-type Faint Attack & Night Slash; Normal-type Quick Attack and Guillotine; and Bug-type Fury Cutter, U-Turn, & X-Scissor. Tactical you have Sword Dance to increase Attack but that's really the only one that stands out.
Moveset Analysis (TM/HM):
Being we didn't have STAB in the learning moveset lets start with them first. Ground-type Earthquake & Dig (STAB); Flying-type Aerial Ace (STAB); Steel-type Iron Tail & Steel Wing; Fighting-type Brick Break; Poison-type Sludge Bomb; Rock-type Rock Tomb, Stone Edge, & Rock Slide; Normal-type Hyper Beam, False Swipe, Giga Impact, & Strength; and Dark-type Payback & Dark Pulse. Tactical we also see Sandstorm which Ground-types won't get hurt from, Roost for healing, and something new in Stealth Rock.
Moveset Analysis (Breeding):
Poison-type Cross Poison; Fighting-type Counter; Normal-type Double Edge, Feint, & Razor Wind; Steel-type Metal Claw; & Flying-type Wing Attack. We also have Baton Pass here too.
Moveset Analysis (Tutoring):
Water-type Aqua Tail; Ground-type Earth Power (STAB); and Flying-type Sky Attack (STAB).

I'm sorry, but with a higher speed, can do an attack that can do quadruple damage, and the other Pokemon not knowing any damage that can be super effective, Gliscor will be Fire Fanging Scizor to death.

MY CHOICE:
GLISCOR
(Wow, for once Ash actually has the adventage)

Scizor: 1 | Gliscor: 2