How can I repair my bench grinder?
If the wheels are wobbling, that could be either a symptom or cause of other problems. A symptom, if the wheel is wobbling because a bearing is bad or because the wheel has been damaged. A cause, if an unbalanced wheel caused excessive wear on a bearing.

As far as affecting the work goes, the answer is yes. There's no way to put a straight face on a wheel that's moving in an arc.

As for fixing it: if the problem is a damaged wheel, then you could replace them. But if the problem is a damaged shaft/bearing, then it's pretty much shot, and the new wheels would be wasted money.