From oregonfirearms.org
If you buy a gun from a licensed dealer in Oregon, a background check is performed by the Oregon State Police. At that time the make, model, caliber and serial number of the gun is recorded, along with all your personal information. In that sense, the gun has been "registered." However, in private transfers, there is no such background check required, although you can conduct one voluntarily if you really think the State Police need your $10.00. This IS NOT required by law unless your transfer takes place at a "gun show." So unless you have chosen to conduct the (entirely voluntary) background check, there is no "gun registration" in Oregon. If you move here with your own guns, or have acquired them from a private party in Oregon, there is no "registration" of any kind and no permits to own or transport. The only "permit" in Oregon is for concealed carry.
This should answer your question
AFS