ninja outfit gives you a different sword attack simply attack while holding one, the strong attack is also different
The psycho outfit gives special animations with certain weapons strong attacks.(Machete, meat cleaver, pitchfork etc...)
The soldier outfit gives you a special hipfire animation with automatic weapons only, and doubles ammo of all fire arms(pistol,shotgun, sniper, assault rifle, LMG (not sure about BFG))
The sports outfit, lets you drink alcohol without puking, and gives you a special charge with the football.