There are several references and someone, hopefully a NAT region ATCO, to link to them. But, random routes can be requested by the flight planner for the operator and can be any legit waypoints or lat/long coordinates in 10 degrees of longitude.
As to the 15nm offset for contingency situations, the crew must first align themselves with any tracks that are in use, them offset and descend. When the track system is active, most random routes are either above or below the established levels, typically FL310 thru FL 400, I think. I do most crossings above the system at FL 430- 470 and briefing and planning the descent is a normal procedure.
GF