All locations on this page are in Oklahoma City.
The trend in fast food is that most McDonalds, Sonic Drive Inns, What-a-Burgers, Jack-in-the Box's and Taco Bells are open 24 hours. I will get the exact addresses posted here as I can verify that a location is open 24 hours or to at least midnight.
Whataburger
3600 N May Ave, 405-946-7177
1325 S Meridian Ave, 405-949-2437
5832 NW 36th St, 405-947-6131
Picture credit: Oklahoma City Farmers' Market, 1900, 100 block of West California. Courtesy of Doug Loudenback.