If 4 years ago my car was stolen and involved in an accident but I only recently found out I have a judgement against me, is that legal?

It is legal, but you should be able to get it vacated as against you.
It is legal in the sense that a car's owner is, on the face of it, liable for any accidents his or her car was win. Since it is a valid claim on its face, if the other side did their paperwork properly, they could get a judgment. 
However, judgments may be vacated (voided or set aside) due to either procedural irrelegularities--if, for example, you were never in fact served with the papers for the lawsuit and can prove (or at least credibly testify) that they went to the wrong address or were accepted by some other person who never gave them to you--or because there is ultimately no merit to them--such as if you can show that even though you were ostensibly the car's owner, it had been stolen when the accident occured, since you are not responsible for what a thief does.
So you should have one or two grounds to get out of this, but will want an attorney to help you, since you need to understand the procedural/court rules to vacate a judgment. If the judgment is for $20k, an attorney is well worth the investment.
Note that IF if you did receive the lawsuit papers properly and in time but ignored them for some reason (e.g. thinking that you could not be responsible) it may be harder to vacate the judgment: even when you think a case is not valid, you are expected to respond to it, and would have to show a compelling reason why you did not.
Or if you never informed the authorities that the car was stolen, or the date you told them that it was stolen is after the date of the accident, that would also hurt your chance of getting the judgment vacated, since it would undercut the fundamental idea that the car was not then under your control.