I have a 1997 Cavalier thats a 2.2 and its running really rough.

May be water in the gas tank try to run a gas line antifreze thru it like heet brand

try going to cavalier repair.com

Check the fuel/air sensor and air filter. When you first start the car only press the accelerator pedal once. If while turning the ignition switch you here a grinding noise that would be your starter going out. The smell of fuel signals that your car is either flooded from pressing pedal or fuel mixture is incorrect. Hope this helps.

It's kind of something telling you that your battery shot. The battery isn't pushing out enough amperage to have things properly function. Replace the battery if the car will not start again after running for about 2 minutes

You should probably sell it before it gets worse. Sounds like it may be an electrical problem that would be a really easy fix if it didn't require the engine to be moved out of the way.

If you can have the fuel pressure checked and compared to factory specs.There may be a leak in the line or where the fuel line connects to the filter.Your going to have to follow the fuel line visually from the fuel rail/injectors to the tank and check for dripping or moisture.I beleive it may be either that or the fuel pressure regulator.

you need a mech you have a draw whitch meeans something is on at all times or internal short on something or pass bad batt.
make sure things ore off like dome light trunk light cig lighter out of socket cell phone charger etc. good luck

Have they checked your TPS sensor as this is the most common cause for rough idles and stalls...

You may be looking at dirty injectors. I would run a good quality (something like Wynns or Redline) fuel system cleaner through, following the directions on the bottle twice. Which usually means adding the bottle to a full tank of fuel, and then adding another bottle after a second fill. Check for improvement, this will cost under $30, vs a trip to a mechanic. A friend of mine had a 2.2l in a sunfire that did something very similar and a good cleaning cleared it up completely. Unfortunately, he spent $300 at a mechanic to find out.

it sounds like the check valve in the fuel pump is letting the fuel bleed back into the tank