95 3.4L V6 camaro surging and backfiring

Hey guys. my car jerks front to back when i accelerate. it hesitates when i step on it and the surges back and forth all the way up through the gears. getting terrible mileage also. 129 miles out of a full tank, so i'm trying to figure out if it just needs a tune up or fuel filter or what. i just bought this car and it was good for a month and now this. rear differentials are leaking too, would that make it jerk like that? any advice would be most appreciated. thanks! whoever had this car did not do any mainteneance on it that much i know.