A few moves you may want to use:
Fire Tackle
The user coats itself in ice and charges at the opponent
Type: Fire
Power: 95
Accuracy: 100
PP: 15
Category: Physical
Effects: Inflicts damage, no secondary effect.
Lightning Slam
The user coats itself in ice and charges at the opponent
Type: Electric
Power: 95
Accuracy: 100
PP: 15
Category: Physical
Effects: Inflicts damage, no secondary effect.
Glacier Charge
The user coats itself in ice and charges at the opponent
Type: Ice
Power: 95
Accuracy: 100
PP: 15
Category: Physical
Effects: Inflicts damage, no secondary effect.
^Basically just physical equivalents to Flamethrower, Ice Beam and Thunderbolt.
Bloodsucker
The user bites the foe and drains their blood
Type: Poison
Power: 70
Accuracy: 95
PP: 10
Category: Physical
Effects: Restores half the HP inflicted to heal the user.
Fake Thunder
The foe is hit with a non-lethal shock of electricity
Type: Electric
Power: 50
Accuracy: 100
PP: 25
Category: Special
Effects: Always leaves the opponent with at least 1HP.
^Because it hits Rock, Steel and Ghost types neutrally, which False Swipe does not.
Featherblade
Razor-sharp wings strike the foe
Type: Flying
Power: 90
Accuracy: 100
PP: 15
Category: Physical
Effects: Inflicts damage, no secondary effect.
Tornado
The user whips up a devastating tornado
Type: Flying
Power: 120
Accuracy: 80
PP: 5
Category: Special
Effects: Inflicts damage, no secondary effect.
Sprint Attack
Strikes the target at its highest speed
Type: Normal
Power: -
Accuracy: 100
PP: 10
Category: Physical
Effects: Deals more damage the faster the user is.
Waves
A series of waves crash against the opponent
Type: Water
Power: 20
Accuracy: 100
PP: 20
Category: Special
Effects: Hits 2-5 times in succession
Plug In
The user plugs itself into the user to drain energy
Type: Electric
Power: -
Accuracy: 100
PP: 15
Category: Status
Effects: The same as Leech Seed, but affects grass-types also.
Energy Bullet
The user fires a small bullet of energy at the foe
Type: Normal
Power: 35
Accuracy: 100
PP: 30
Category: Special
Effects: Inflicts damage and has no secondary effect.
^For low-level pokemon with higher special than attack, that would otherwise be lumped with Tackle.
Mountain Storm
Fires a blast of rock dust at the enemy
Type: Rock
Power: 100
Accuracy: 90
PP: 10
Category: Special
Effects: Inflicts damage and has no secondary effect
Aftershock
Strikes the foe, with an added shock afterwards
Type: Fighting
Power: 65
Accuracy: 100
PP: 20
Category: Physical
Effects: Damage is inflicted. Then at the end of the following turn, after all moves have been used, ½ the damage originally inflicted is inflicted again. Eg:
Poliwrath used Aftershock! (lets say 40HP is deducted in this instance)
Scizor used Slash!
Poliwrath used Waterfall!
Scizor used Bug Buzz!
Foe Scizor is hit by the Aftershock! (In this instance, 20HP is inflicted)
That's all the moves I have so far.
Can I also suggest an additional weather effect? Night-time. Dark and Ghost type moves are boosted, while Grass moves are less effective. Moonlight heals more HP, and Synthesis heals less. The activating move would be "Sunset". Some nocturnal pokemon like Hoothoot would have an ability called "Nocturnal", which would boost their power during night-time, but reduce it in bright sunlight.