I'm in the Active Duty stationed in CALIFORNIA but resident of OKLAHOMA.  Can anybody point me in the right direction for information regarding rules applying to me regarding an AR-15?

Keep your rifles at home. (In OK) The same rules apply to you, even if you are from out of state.

If you REALLY want to you can either pack out the weapons in your pack out or do a DITtY move and pack them yourselves to the base where you are stationed at. The base commanding officer must allow these types of weapons to be stored in the armory on his base.
The weapons must never ever leave the base unless you are PCS'ing out of state.
You can only shoot them on base.

I was living in Oklahoma, I was up for orders before the Kalifornicommiecation SB23 bill was passed.
I sent a letter to the CAL-DOJ and asked how that would affect me.
I was told that (too late for you now) I could bring any "assault weapon" into the state provided that I owned it before the cut-off date, and that if I wanted to use in I had to register if as an "assault weapon" with Kalifornicommiecation.
The letter also stated that I could bring my "assault weapons" into the state without registering them IF they were stored on the base and never left the base unless I was PCS'ing.
It sounds to me like you should leave your Kalifornicommiecation defined "assault weapons" in Oklahoma, and buy yourself a nice Garand M1 for shooting in Kalifornicommiecation.