Everyone has seen the infamous Portlandia skit.
Despite what you may have learned in driver’s education about four way stops in Oregon, the person who stopped first or the person to your right does not have the legal right-of-way. Neither does the person going straight have right-of-way over the person turning left if they are not already in the intersection. The only person who has the right-of-way at a four way stop in Oregon is the vehicle operator who is already in the intersection.
ORS 811.260(15) Appropriate driver responses to traffic control devices contains the controlling law for a vehicle operator facing a stop sign.
(15) Stop signs. A driver approaching a stop sign shall stop at a clearly marked stop line, but if none, before entering the marked crosswalk on the near side of the intersection or, if there is no marked crosswalk, then at the point nearest the intersecting roadway where the driver has a view of approaching traffic on the intersecting roadway before entering it. After stopping, the driver shall yield the right of way to any vehicle in the intersection or approaching so closely as to constitute an immediate hazard during the time when the driver is moving across or within the intersection.
There is no right-of-way for the vehicle approaching from a vehicle operator’s right at a controlled intersection like that found in ORS 811.275 Failure to yield the right of way at uncontrolled intersection for uncontrolled intersections (a topic for another day).
The Oregon Driver Manual says
At any intersection with stop signs in all four directions, it is common courtesy to allow the driver who stops first to go first. If in doubt yield to the driver on your right. To avoid the risk of a crash, never insist on the right of way.
2014-2015 Oregon Driver Manual, page 44. Emphasis added.
So the next time someone waves you through you can proceed knowing you are not snatching the right-of-way from them. Once you cross your vehicle over that stop line and into the intersection that right-of-way is legally yours.