Here's the way it works:
1. You file for divorce where you live. You need to establish residency in OK before you can file there (you don't get to choose). The rule in OK is "Either the plaintiff or the defendant in an action for divorce must have been an actual resident, in good faith, of the state, for six (6) months next preceding the filing of the petition." (there is an exception for military) So if you've been in OK for 6 months, that's where you file.
2. If you have NOT been in OK for 6 months, you have a problem. Let's say you both lived your entire life in TX and both moved to OK 3 months ago. Legally, you are not an OK resident and can not file there. You are also not a TX resident so you can not legally file there. So, you will be in 'limbo' and unable to file for divorce anywhere. Of course, many people cheat a bit by saying that they're still a resident of the previous state, but that does require lying to the court.
3. The divorce property division rules will be based on the state where you file. Take the simplest case of two couples who each own homes that are solely in the husband's name. Both homes are in Texas, but one couple is a resident of OK and the other is a resident of TX. For the couple who lives in OK, Equitable distribution rules would apply. The couple living in TX would be bound by community property rules. It's the divorce court which determines the property division, based on the rules in that state.
4. Since OK is an equitable property state, you may be making a mistake by looking solely at the home. Let's say that both names are on the deed, making the home equally owned by the two parties. In OK, the court can say "the home is equally owned by both parties, but the wife contributed $100,000 down payment while the husband did not and they both contributed equally to future costs, so we're going to give the wife a larger share of the other property to make up for it". They can do that even if the home is in TX.
5. Keep in mind that the divorce court will not (usually) actually change ownership of the property. If the court says that husband gets the property and must pay the mortgage, it is up to the couple to do the paperwork to make that happen. Ideally, husband would refinance and wife would sign a quit claim deed at the closing table.
ETA:
6. Both states allow truly separate property to be excluded from the divorce settlement. TX seems to be a little strange here.
Explanation of Texas community and separate property
That is so different than the way most states work that it needs to be considered carefully - and I would definitely check with a local attorney before doing anything. However, another site seems to support that:
The Significance of Separate Property in a Divorce in Texas | Information Provided by a Houston prenuptial lawyer
Essentially, if I'm reading the law correctly, if a home is purchased before marriage by one party, even if community income is used to pay for the mortgage, the home itself remains separate property. That is based on reviewing a number of cases. The only significant exception I can find is the concept of 'enhancement'. If community property enhances the home owned solely by one person (major upgrades, adding an addition, etc), then the enhancement remains community property while the remainder of the home value remains separate.
That is so different than the way that most states handle home ownership, that I hope garrula will have a took and correct me if I'm wrong.
