According to the Nebraska State Patrol's website, they changed their law and recognize certain out of state permits, including Oklahoma.
Here's the link:
http://www.nsp.state.ne.us/FindFile.asp?ID2=256
Scroll down almost exactly half-way to the out of state permit section.
Here's the link:
http://www.nsp.state.ne.us/FindFile.asp?ID2=256
Scroll down almost exactly half-way to the out of state permit section.