My wife and I live/work in Texas (rental), and are considering buying a home in Oklahoma as we plan to settle down there in a few years, considering I won't be living in the house OR earning money in the State of Oklahoma, will I owe state income tax

No you will not since you will have no income from OK and OK will not be your state of residence  so don't homestead the property. 

If you move from state A to State B mid-year, with the intent of making state B your primary residence, then you will be filing two state tax returns *if* both states tax personal income. Both state returns would be part-year resident returns and a non-resident return would not be involved in this scenario.

In your case, since State A (Texas) does not tax personal income, I believe you would be filing a part-year resident return for State B (Oklahoma) only. State B will tax all of your world-wide income earned from the time you became a resident of state B.