Oregon issues six distinctive license plates honoring service members, veterans, retired service members and certain family members. Each plate has its own eligibility and documentation requirements. The plates the source describes individually are the Medal of Honor, Disabled Veteran, Veteran Recognition and Gold Star Family plates.
Start at the Oregon DMV license plates webpage to see the plates and how to order one, then submit the certification form for the plate you want with your proof of eligibility.
Proof of eligibility for the specific plate, which is usually your DD214 or DD215, plus the completed certification form for that plate.