Biggs: Biggs occasionally acts as Jessie's partner, by finding and punching in codes for mechanical locks. He has a good heart and is, what I believe to be, second in command of Avalanche.
I've heard rumors that he is suppost to be some kind of Fighter/Ninja, but who can tell?
Jessie: Jessie is the brains behind Avalanche. She can build anything from fake ID's (to pass through SHINRA's Scan checks) to bombs capable of destroying entire cities!
I believe her fighting style is Kick Boxing, she side kicks a soldier in the very beginning of the game.
Wedge: Wedge is the tag along member of Avalanche. He mostly just watches for in-coming soldiers. Wedge isn't among the best of fighters, he is also the slowest and worst at desgiuses. He dresses as some strange kid while Jessie is in a Soldier's uniform and Biggs is in a trenchcoat. But you have to give him some crdit for surviving a fall off a 10 story pillar!
Wedge doesn't actually fight in FF7, so my guess is as good as yours.
