I have a question for those of you with some audio-editing experience: I'm doing some of the initial sound effects for my game and I want some of them to have an echo effect that makes it sound like they're coming from all around you, as opposed to from a specific direction. Yet, this seems to be a little more complicated than just copying the effect once or twice and shifting both its pan and timing, so I'm wondering what advice everyone has on doing such an effect and making it sound really good.

Reverb and EQ'ing higher frequencies (reducing) can help to give the impression of distance, combine that with panning (look up 3D equalisation); very basically:

"Left to right stereo spread is the horizontal plane (x), the entire frequency spectrum is the vertical plane (y), and front to back is your depth (or z plane). You work in the X plane with the stereo pan positioning, the Y plane with equalization, and the Z plane with time based effects such as reverb and delay and the wet/dry balance of those effected tracks"

IIRC, sounds are perceived to come from front or back because echoes from surrounding objects stay the same, but the primary sound waves aren't focused by the outer ear when coming from behind.

Once I created a stereo effect, where I got the whole stereo image rotating around. It was like all musicians were standing in a half circle and then the circle started to rotate. Center panned players moved to the left, as well as the far right panned players, while the left panned players started to move to the right. Each player oscillated back and forth between far left and far right, in their own phase. I must have mentioned it on this forum. Though I never implemented it in Audacity. Only in A4.