Yes, you can appeal a Small Claims judgment in Oklahoma.
"If you do not agree with the decision rendered against you, you have the right to appeal. This appeal would go to the Court of Civil Appeals, and then, potentially, to the Oklahoma Supreme Court. In these appeals, however, you would be held to the same formal pleading requirements, including the necessity for citations of legal authority (case law) as an attorney. This can be a costly and time-consuming process, taking up to two years to resolve. Often, however, you will be required to post a bond to cover the Plaintiff's losses if your appeal does not succeed. "
This is covered under Oklahoma, Civil Procedures, §12-36-1763:
"Appeals may be taken from the judgment rendered under small claims procedure to the Supreme Court of the state in the same manner as appeals are taken in other civil actions"