I applied for 3, got all three and only went on 2. From my experience, it seemed more like a first come first served process than a competitive one.
My best advice to you is that if you aren't hearing back about an application, call the ortho coordinator. I was accepted to two of my Away rotations over the phone when I took the time to call them and ask if there were slots available, or all filled, or still processing. Obviously don't call daily and annoy them, but definitely give them a ring after you've gotten everything in just to check up on things.
I would not take a "shotgun" approach to away rotations,you'll likely get more than you can go on.