Interesting discussion. Since I haven't read the driver's manual since I got my permit 50+ years ago
I looked up the manual on the ODMV website. It doesn't really say much about 4 way stops other than look both ways and in front and proceed when it is safe to do so. I was always taught basically "first in - first out" but it doesn't say anything about that in the manual.
Other interesting comment I saw was that the right-of-way laws do not establish who has the right-of-way, but who must yield. Off to find the laws............
(11)
Flashing red signal. When a driver approaches a flashing red light used in a traffic control device or with a traffic sign, the driver 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. The right to proceed shall be subject to the rules applicable after making a stop at a stop sign. This subsection does not apply at railroad grade crossings. Conduct of a driver approaching a railroad grade crossing is governed by ORS 811.455 (Failure to stop for railroad signal).
(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.
IOW while there are some common courtesy things like first-in-first-out, and if in doubt yielding to vehicle to your right, it would appear that whichever vehicle enters the intersection first has the ROW.