Um, Quilava does NOT learn ember! (Cyndaquil does! lvl 7 or 8)
The moves that Quilava can learn are Leer, Smokescreen, Tackle, Ember, Defense Curl, Flame Wheel, Swift, Lava Plume, Flame Charge, Inferno, Flamethrower along with Rollout, Eruption and Double-Edge.
Yes, Quilava is able to learn Strength.
quilava learns flame wheel,double edge,flame througher,smokescreen,ember,lava plume,focus punch that's all i know
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You can check what moves Quilava can learn here: http://bulbapedia.bulbagarden.net/wiki/Quilava_%28Pok%C3%A9mon%29#Learnset
Cyndaquil doesn't learn anything really useful until it evolves into Quilava. I would say the best thing it learns before it evolves would be ember, but i suggest that you look it up on the online pokedex to fully figure out what moves it learns.
Lillipup cannot learn ember.
Tepig learns ember at level 7.
Quilava will evolve in to typlotion at 36 before it gets the attack Flame-wheel at 41.Mr.Seidschalg
Cyndaquil/Quilava/Typhlosion learn Flamethrower at lvl 42. You can also get the TM for Flamethrower from the Game Corner for 10,000 coins, but do not recommend that on account of going insane with boredom.
Actually if you want you can pick cyndaquil in the beggining of the game and quilava can learn cut
Can't, Ember is Fire and the Herdier is Normal