If a divorce and child support are finalized in Oklahoma can jurisdiction be changed to the state of Texas when one party lives in Oklahoma and one in Texas?

Yes & No. All US states recognize the legal validity of all marriages, divorces, custodial, child support and other domestic issues where a court order has been issued. So the original court order will stand.

However, you can file an amendment or modification to the existing order. For example, if the children establish residency in Texas by residing in a Texas county for more than 6 months (you must show proof) - you can establish jurisdiction for any legal matters concerning the children. You would then have to "transfer" jurisdiction of the case the local court from the original court, and file a motion to modify the order.