Actually, if the transaction is between two private parties, both of whom are legally allowed to purchase guns and both are residents of Oregon, there is no paperwork required.
http://www.nraila.org/gun-laws/state-laws/oregon.aspx
“... Any person who transfers a firearm at a gun show is required to request a criminal background check before completing the transfer. Any person who transfers a firearm at any location other than a gun show may voluntarily request a criminal background check before completing the transfer...”