As I understand it, omnidirectional and non-directional both indicate that something:
...is not affected by direction in any way
So are these two word equivalent in meaning?
Omnidirectional and nondirectional are very similar, but they emphasize different things. If I say something is omnidirectional, I'm emphasizing the fact that all directions are equal. For example, I could be in front of, behind, to the right or left, on top of, or underneath an omnidirectional microphone and it could pick up sound just as equally from any of those directions. On the other hand, nondirectional carries a connotation that direction isn't that important—a sidewalk is nondirectional because I can walk either way without coming upon restriction, but there's no reason to emphasize the fact that I could walk any which way I wanted to.1
1 Which would, for the record, be a very bad idea, because of the narrow width of the sidewalk and the proximity of the actual road with motor vehicles bearing down upon you.