This year I ended up spending a total of about two months out of the state on orders for work (full time National Guard). Someone mentioned that I might be able to get reimbursed for my Oregon State income tax that was deducted for the months that I was working elsewhere. I am wondering if this is at all accurate, and if so, how do I do that?

That is NOT accurate. Temporary work outside of the state of residence is STILL taxed by the home state.

National Guard service by law is NOT subject to taxes by the non-home state where the duty is performed, so there is NO double taxation.

Now, if you served outside of the United States in a war zone (anywhere in southwest Asia), THAT income is tax-free by the IRS and possibly by the state of Oregon. An email to the Oregon tax department should get you answer on that front.