... like, for example, having your ship be in a solar-wind-like area of space, so that it looks like being in warp transit... how do you do that?

In that particular case, there is an asset that gets put on the map that causes that effect, it might be a background. There are tons of little tricks that the more experienced authors use.
A lot of great advice can be found in the chat room at StarbaseUGC.Com. The people there are very helpful, and friendly.

And sometimes a little bit wacky

Nah, warp trails are a weather effect iirc.

There's two different ways as I recall. One is the weather effect (scroll down the details tab until you get to the weather effects) and the other is to make a custom backdrop. Warping stars is one of the options. They both look different. The advantage to the detail version is that you can turn it on and off.

The effect is Star Streaks West - East 01. The other Star Streaks are not as good. It only works west to east, it doesn't matter if you rotate the push pin or not, so be sure to plan your map out accordingly (although now with multiselect in the worst case scenario you can just select everything and rotate it as necessary).

To make it so the player can't leave the Star Streaks effect you must put invisible wall talls approximately at +2/-2 Z compared to where the Star Streaks effect is. In addition, you need to set the Y value on the invisible walls to -20, so that the player can't go under them (the wall starts at it's Y value and goes up from there).