Learn English – the difference between “irreligious” and “non-religious”

Skeptical means “having reservations”. Someone who is skeptical will not easily be convinced, will be hard to persuade.

The main meaning of cynical is “believing the worst of people”, or as NOAD says, “distrustful of human sincerity or integrity”. By extension, it has come to mean “doubting something will happen”, which can be somewhat close in meaning to skeptical in some cases, but not generally.

As an example, in the sentence “John is skeptical about the motorway extension”, you could replace skeptical with cynical without altering the meaning. In the sentence “John is skeptical about global warming”, you could not do this change. Likewise, in “John has a cynical attitude”, you could not use skeptical instead.

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.