So I've been fighting different wolves, and recently I've been fighting players that have these scary sounding attacks. Are these really a big deal? Are they stronger than the level 1 options? More accurate? I'm not sure I've noticed a big difference aside from Strangle Hold having Off + 6 intead of Off + 1.

Heres a guide about battle moves :)

Alright. So the battle options affect accuracy. It didn't seem to be damage. Biting and decapitating somehow hurt a wolf the same with equal stats.

Yeah, all moves hit exactly the same damage. Now, when your wolf reaches certain moves, it can increase your damage in total (so after learning these moves, your wolf will hit that amount of damage no matter what move you set it to)