As a native Californian I definitely use "up" and "down". Up to L.A., down to San Diego. I might make a trip up the coast to Oregon or Washington. I also might go back east (meaning the east coast). Never used "out" though, probably because I'm already about as west as you can go on this continent! "Over", however is just used without regard to direction, though it generally signifies a close distance. I'd head over…
As a native of... nowhere in particular, I think "up" and "down" are pretty universal among Americans for "north" and "south." I wouldn't be surprised if they're near-universal to inhabitants of the northern hemisphere, since that's the way maps are drawn. A possible exception would be inhabitants of mountainous regions saying e.g. "up to Leadville" or "down to Denver." Having lived in Houston, I didn't notice "over"…
The whole out and over thing seems more regional to me. In Australia "out" is generally just "far from here" and "over"... well that isn't a thing, at least in the dialects that I'm used to. :-)