Is there a statute of limitations on a misdemeanor warrant in the state of missouri?
There is no statute of limitations for a warrant. They never expire.
The best thing to do here is to contact an attorney in the area where all of this happened; he will have contacts in the prosecutor's office and will best be able to sort this all out for you. Missouri in all likelihood won't pursue you on this; however if you are pulled over for a traffic violation or undergo an employment background check this could, and probably will, all turn up (no matter what state that you might be in at the time).
You interests will best be served by turning yourself in to the court voluntarily. If it's for a misdemeanor, whatever the penalty it will be nothing compared to having to look over your shoulder for the rest of your life.