While most vehicles are prohibited from passing another vehicle on the right in Oregon, bicyclists are allowed a special exception.
ORS 811.415 makes it clear that all vehicles can pass on the right in some circumstances (the other vehicle is turning left or the vehicles are in separate lanes (even bike lanes)). The law goes on, however, to allow a bicyclist to pass on the right in all other circumstances so long as they "may safely make the passage under existing conditions".
What does that mean? "Safely" is not defined in the law. A good rule of thumb is to not pass on the right when it is clear that another vehicle intends to turn right or is making some other maneuver that could be reasonably interpreted as making the passage unsafe.
This maneuver is frequently used to pass stopped cars at a traffic light or stop sign (or simply slow or stalled traffic) to allow bicyclists to pass to the front of the line.