The fact that your employer is not licensed to do business in Oklahoma is an issue for your employer more than for you. So I suggest that your first step should be to talk to your employer's HR or legal department and ask whether or not they would permit you to work remotely from OK.
The issue is that having an employee in OK might create "nexus" in OK for the company, and subject it to the tax laws of Oklahoma, both state and local.
I suspect that this would not be a problem if you were paid as an independent contractor, rather than an employee, but I'm not sure.
@rjs is totally correct that any income you personally have from working in an Oklahoma location is fully taxable by Oklahoma.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
