Quite a few of the routes go both directions, but they'll be numbered consecutively. So VR 1010 (I'm making this example up, BTW) might be one set of points, flown clockwise or east to west or whatever, and VR 1011 will be the exact same groundtrack, but in the opposite direction (west to east or counterclockwise or whatever).
Where I used to instruct we used SR-137 quite frequently, but we could have just as easily used SR-138... same route, but flown the opposite direction.
Exactly. Plus, the aircraft you may have seen going the opposite direction could've been in the LATN area, ie- where you can fly anywhere low-level, and not necessarily on a designated route, since in that area of the Sells MOA, both exist.