Is it legal to drive with a Japanese driver's license in Oklahoma?
If you have an International Driver's Permit, yes. Go to any Menkyo Center with your passport, current license, the usual picture and about ¥3,000. One form, 30 minutes. Ask for the "Kokusai Menkyo" counter.
Note that the testing center that issued your license is not the same as a place that renews licenses. Both will have international permits, so use whichever is convenient. If you speak enough Japanese, just ask at the local Koban for the closest place.
In addition to an international license (which is just an addon to your regular license that provides translations in several languages including English), you also have to check local laws regarding how long you're allowed to reside in the state without having to apply for a local license.
Several (maybe even all) US states require people staying for more than a number of months to apply for a locally issued driver's license (and possibly other paperwork regarding your residency).
Shouldn't be a problem if you're there for a few days or weeks as a tourist, but if you're going to the place for several months to work as an expat you may have to take steps. In that case, the HR department of the company you're working for will likely be able to assist.