You have a legal question (more for your company than you), not a tax question. It may depend on the nature of your work is nature of your work. If you're only doing office work from home and not calling on local customers or manufacturing something, your company doesn't usually need to be licensed in that state. But, then there's that "nexus" thing.
I'm not sure what the statement " the company is only licensed to work for tax purposes" means. If it only means they won't be able to withhold OK state tax from your pay; that's not important. You just have to make estimated tax payments to OK on your own.
As others suggessted, start by discussing it with your employer.
