I do not practice in OK, but suspect that the situation is similar nearly everywhere.
If there is a warrant out for you, you can be picked up at any time. If you want to avoid the possibility of the police swooping down on you today, tomorrow or when you are picking up your kid from school, you will want to turn yourself in on the warrant(s). The court is more likely to respect the fact that you turned yourself in, as opposed to being forcibly brought to court by the police.
Turning yourself in will sometimes go more smoothly if you have an attorney who can walk you into the police station and arrange to be in court when you are brought in after being processed. (You also do not want to talk to the police about the case at all and having an attorney will help motivate them not to ask you questions.) Bring the amount you owe, bring some extra money for bail in case you need it and bring proof of how you are doing in your life.
You are correct that the checks will need to be paid back, and the best proof of your good will in that regard is to have the money ready to pay them back in full. Whether or not the victims would take your money and give you a receipt, this would not resolve the criminal case(s) against you on its own. You probably need to turn yourself in to get the warrants vacated and the threat of arrest lifted. You will likely not know how many charges are actually out there until you go in and start dealing with them.
It may be that, in your jurisdiction, there is a way for an attorney to appear for you. I don't know. Talk to some local experienced criminal attorneys and they should be able to answer that question.
DISCLAIMER: I do not practice in OK. This answer to a short question is provided solely for general informational purposes and based on general legal principles and court practice. This answer does NOT constitute legal advice, create an attorney-client relationship, or constitute attorney advertising.