Engine problems with my 1990 Dodge Omni.?

Question

The most recent computer code I got from my car was a 51. Which is the O2 sensor being stuck on lean position. When I purchased the car used, it was not running, the catalytic converter was plugged up, smoke and exhaust was pouring from the engine and the engine was shaking erratically when we tried to start it. We unplugged the catalytic converter and it started it and it worked fine, to take it home and find out that one fuse was bad and the oxygen sensor was bad. I replaced the oxygen sensor (it was from a wrecking yard but it was fine.) Over time I've found the car has developed problems with the engine vibrating more than it should while it's idling. I can smell exhaust and I'm getting very bad gas mileage. So my guess is that SOMETHING is causing the oxygen sensor to go bad. We replaced the map sensor, but nothing changed.
If an O2 sensor is stuck in a certain position can it fix itself or is it pretty much done?
Could it be the computer? Where can I find a computer for my car?

Also, I drove it today when it was fairly cold. When I was backing up the car started to do some jutting. The person I bought it from said it stopped running after a cold snap.
Any ideas will help. Thanks!

I won't be getting any other vehicle.
I love my Omni.

Oh yeah, we did replace he catalytic converter because the other one had all the ceramic punched out so we could get it home.

Answer 1

Where did you get 51 ? I can;t find any codes from the 90's that are two digit for chrysler products. If we have a bad code we are getting bad info.
O2 sensors don't get stuck and an O2 code for lean means just that, your engine is running lean. This will also cause your engine vibration caused by misfire from lean condition. Changing sennsors is not the cure. The lean condition means you are not getting enough fuel or you are getting too much air. check the throttle position sensor (tps), check the throttle valve in the throttle body and check the throttle body for dirt etc. Also could be dirty injectors.

Answer 2

"Catalytic Converter!" Started with and still is! You need to Replace the Converter and the o2 sensor, Both from A Parts Store or the d Dealer (Junk Parts!) Electronics, when a Sensor is bad it's bad "Junk"

Have a Muffle Shop Check, You may need a Muffler too.

Answer 3

you can replace o2 sensors no problem. If your ride feels like it is missing a cylinder fire you could have a bad spark plug or spark plug wire. I would spend my money on a newer vehicle and start over with something that just needs a tune up. If you are looking for a utility van a newer chevrolet astro van can be a good choice.