When you're in the air, you have more maneuverability. When you SH, you can move greatly according to what your opponent does, and using a projectile limits, or changes their approach. Also it's faster, ever notice why samus mains SH missle why mario and luigi SH fireball, why falcons SH raptor boost or falco's and fox's SH and do their illusion dash thing (the name is slipping me), why pikachu's SH tjolt, and so on. It's not olimar exclusive. There is more maneuverability, less lag.
As for DI, look at the vid, it helps a lot. DI perpendicular to the stage, and momentum cancel. For olimar's... I've found it's easiest to use uair for momentum cancel. I laughed at zori, but frame data says it's just as fast as fair, and the uair is a besst (and easier) fast fall.
EDIT: Not self proclaimed btw. In omaha, in comparison to shrink ray, most people said I was better. All but 1 if you exclude crew bias. I've also had this given to me at every tournament I've gone to. So I've just stuck with it. Most people agreed at omaha that I was the best olimar there... and I've gotten better since then
~Fino
Most of those characters short hop their projectiles to give them a funky trajectory or because it has less lag that way. Olimar is a little different, though, in that his projectile (usually) does not have a hit box. So if you jump and toss a couple pikmin fast characters (or mortar sliders) can sometimes get to you before you hit the ground; this isn't as much of a problem for other characters because their attacks will stop the other player's advance (or at least force them to shield, which gives the jumper time to land). Olimar is also weaker in the air than a lot of characters, so he is sort of vulnerable if you jump.
I'm not saying tossing from the ground is always better, or even better most of the time, but I think it is better sometimes. Like, if you're running away then I think it is often better because now you're facing the other player, so you can shield, grab, f-smash, whatever, depending on whether they try to avoid the pikmin or just keep coming after you. I also think it is better sometimes when you are at mid-range. For instance, against Snake if you are within range of his mortarslide and you shorthop double pikmin, I'm pretty sure he can hit you with the mortarslide before you're safely back on the ground. Whereas if you were standing then I think you have time to throw a f-smash after the pikmin toss if he mortar slides. I'm just going off the little Snake experience I have, though, so I could be wrong.
By the way, who shorthops their raptor boosts or spacie >Bs? I guess if the Falcon wanted the spike to lead to something else it might make sense, but I never see people shorthop these moves. Not that I've seen many good Falcons or spacies...
Also, you know how to get videos from your SD card on the internet, don't you Fino? You should help a brother out.
As for DI, don't you also want to DI with the c-stick? I thought you held the control stick perpendicular to the way you want to go and the c-stick toward where you want to go? Let me get this straight then: after getting hit you hold control stick perpendicular to the direction you want to go while smashing the c-stick either toward the stage (f-air) or up (u-air). Once you do your aerial you fastfall. Correct?
Lastly, Omaha=/=Midwest, you+Shrink=/=the only good Olimars in the Midwest (and no, I'm not talking about myself).
tl;dr version: I like food.