Testicles facing opposite directions

It sounds like you're describing a testicular torsion but those come with intense pain. It could be that you don't have a full torsion that has cut off the blood flow, or you could just be unique. There is a possibility that after the intense pain of torsion if the blood flow has stopped completely then the testicle could die and there may not be any more pain as a result.

You should probably talk to your doctor about this. If you do have a torsion you need to get it corrected immediately or risk losing the testicle. If you don't have a torsion then at least you know the correct way for them to situated.
 
From what you have said. You could have whats called bell clapper deformity. if your worried talked to your doctor about and ask if thats what it is. Bell clapper deformity does increase your risk of getting testicular torsion.
 
As the title suggests, my balls seem to be orientated differently, based on the tubing coming out of them. One has a certain feature at the front, the other at the back.

Is this something I need to worry about?
Have they always been that way? Definitely go get checked by a doctor