1997 Saturn SW1 Burning Oil

My 97 Saturn SW1 has been slowly burning/leaking more and more oil. I first noticed it when the oil light flashed on the dash. I immediately stopped and bought oil. Eventually, the oil leaked out faster and faster without smoking! So I looked into buying an oil stabilizer. This seemed to help quite a bit. But a few months later, it started smoking out the exhaust, and over 3 days it got to the point where it was undriveable. There is so much thick white smoke that I leave a trail 4 blocks long behind me. Any idea what can be happening? Head gasket?
The other thing the car does sometimes is shudder when idling in gear at a light. If I put it into neutral, it stops.