Was it the actual payday loan company that sued you or was it a collection agency? If it was a CA, you would likely have a cause of action against them for suing you when the SOL was expired.
This does not, however, nullify the original judgment. Depending on the specifics of your actual case, there may be a chance that you were not properly served. were that the case, you'd have to file a Motion to Vacate with the court and they'll likely schedule a hearing to consider the issues. If and when the court actually vacates the judgment, if the SOL had expired before you were originally sued then any subsequent suit would be time-barred.
I would first research the specifics on personal service in your state's civil procedure law. If the old address in which you were served belonged to a relative and they accepted service, it may be considered proper service. Nail & Mail may also be considered proper service albeit to a prior address if the creditor had no knowledge of your new address. Check your state's civil procedure law and then decide if you want to attack the judgment.
