Is the state of Oklahoma even mentioned in The Outsiders?
The state of Oklahoma is only mentioned once in the book. This comes in Chapter 7. This is after Ponyboy has had his hair cut. Two-Bit sees him for the first time like that and talks about how Ponyboy has been scalped. He says he thought all the Indians in Oklahoma "had been tamed" (it's p. 106 in my copy of the book). This implies that they are all living in Oklahoma.
Other than that, the word "Oklahoma" never appears in the book. The word "Tulsa" never does appear. People know that the book is set there because the author has said that she set it there, but it is not really explicitly mentioned.