Honda Repair: Odd noises at acceleration, oxygen sensor, honda civic ex

Question
I recently bought a used 1997 Honda Civic EX. It seems to run pretty good except for shaking (doesn't do it when I go above 30 miles though) however it makes rather odd noises sometimes like today I heard what sounded like a small mini-chainsaw (grinding almost) when I pushed down on the accelerator hard. I wasn't going too fast (40 miles) when I did this either and suddenly I would hear that noise. I've also heard some other noises at acceleration or when maintaining higher speed. It seemed to be coming from the back of the car. Also the engine light is on (but I read thats normal for a Honda) and was on when I bought it but the dealership said it was nothing more than the oxygen sensor (don't remember the exact name).
My question is do you know what that noise might mean and is it normal for the engine light to come on when something might be wrong with the oxygen sensor? Does it damage your car to have a bad oxygen sensor?

Answer
Kelli, it is not good for the check engine light to be on period! Have this evaluated for free at a local auto parts store. Or take back to the dealership and make them fix the problem. If it is the O2 sensor then it is possible it could damage other parts of the car as well. You are also losing gas milage too. Grinding sounds are just odd and hard to locate specifically. Bring a friend along with you on a ride and try and have them locate the area where the sound is coming from specifically on the vehicle. If i had to guess i would say the exhaust or one of the wheels. Grinding usually is an indication of deteriorating brake pads or rotors. But, only under acceleration makes me focus more towards exhaust. Yes, the check engine light will always come on with a bad O2 sensor.