This video shows strategies for the "void" levels (the game calls them "Secrets") in Super Mario Sunshine. All of the strategies I used are the fastest I've seen except when noted, although admittedly I didn't spend much time looking for faster videos because I kept finding red coin videos instead. So, I just looked at the full-game runs by Dragorn, Doodan, and Thiradell. I gleaned several tricks from their runs, so thanks are in order.
There are a few things to keep in mind when playing the voids. One is that the gravity is somewhat different than it is in the rest of the game, so you can stand, run, etc. on fairly steep slopes without sliding. Another is what triggers the platforms that wait for you and then carry you somewhere. They start moving when you either come to rest on top of them or grab one of their edges. You can run around on top of them for hours without triggering them if you want. These properties are illustrated in the first clip of The Yoshi-Go-Round's Secret, where grabbing the first moving orange platform helps me get to another platform later on before it is out of reach, and in the video of The Secret of Casino Delfino, where I waste quite a bit of time by running around on top of the large cube at the end.
I should note that these are NOT speed runs, so mistakes were left in if my intent was clear. Also, the voids were already beaten when I started, but I didn't use FLUDD or the red buttons (the red buttons were actually pretty annoying).
The Hillside Cave Secret: There might be a way to do the end with a little less sliding.
The Secret of the Dirty Lake: There's probably an easier way to do the platforms at the end.
The Secret of Ricco Tower: My favorite void. In the stationary section after the first four rotating platforms, you might be able to squeeze in a dive-flip and do a somersault-dive instead of a triple jump-dive. I'd suggest being a bit conservative when jumping to the biggest rotating platform near the end; it's farther away than it looks.
Dune Bud Sand Castle Secret: I think it's pretty obvious how the end was supposed to go, so I didn't bother redoing this one.
The Beach Cannon's Secret: Your speed is limited here by the reappearance of the row of platforms after the trampolines, so there are a lot of ways to do the beginning of this level. The somersault-dive from the gray platform after said row of platforms probably didn't save any time.
The Yoshi-Go-Round's Secret (hard): I included two videos of this void because I feel that the strategy in the first is impractical in a single-segment run; there is very little margin for error if you want to get to the rising and falling platform near the end quickly enough to wall jump off of it. If you don't get there soon enough, your daring somersault-diving and triple jumping (thanks to AKA for that triple jump at the end, by the way) was for naught.
The Yoshi-Go-Round's Secret (easier): This strategy loses about 9 seconds to the hard one, but is much easier.
The Hotel Lobby's Secret: After breaking the bricks, I should have done another somersault. I'm unsure of the fastest way to get across either set of sand blocks, and the somersault-dive at the end would bring you a little too close to death for comfort in a single-segment run, in my opinion. The ground pound is a cheap way not to go flying past the spinning platform, but I think it doesn't lose much time.
The Secret of Casino Delfino: I made this video before I was aware of the nature of the platforms that Mario triggers, so you can see that I lose quite a bit of time near the end by running around on the big cube.
The Shell's Secret: If you're feeling lucky, you can jump on the edge of the second spinning platform. There are quite a few places in this void where you can use regular jumps instead of somersaults, but I mainly used somersaults to minimize the amount of wall jumping. This is another video where I made a mistake but left it in. In this case, I missed a jump onto the spinning multi-level platform. Once again, my intent was fairly clear.
Secret of the Village Underside: Your speed is greatly limited by the final Pianta, so just take your time lining yourself up before talking to the earlier Piantas.