my main non-recovery use of pika's upB is the bthrow -> QA out and back. Can catch some chars' recoveries, and ends with you grabbing the edge, so you can drop off nair or edgehog or do something else from the ledge.
UpB edgehog is also super useful. Usually I'll do this from stage level, but you can do it from platforms as well on some stages. The main thing to note about this is you can do it from decently far away from the edge (it's the fastest way to ledgehog if you're far from the edge). Also no other char (except pichu of course) can really do this, so it's something extra the opponent has to think about. If they're not thinking about it, it can really mess up their recovery plans. "i'll just fastfall and upB to the edge before he can get there" suddenly becomes "well crap, now I guess I have to upB to the stage? do I still have enough room to make it?"
There's also the superwavedash, which I don't really utilize, but it looks super cool. It's been mentioned a ton of times, so I won't go into it unless you're unfamiliar with it. It can be useful, just have to have super good predictions.
I'll also use it semi-defensively after I've recovered sometimes. Say I got hit offstage, and successfully recovered to the edge, but now there's a marth onstage standing about tipper-length from the edge, and I still have to recover. I can jump from the ledge, but he'll fair me if he reacts to it, putting me back off the stage. I can roll or attack from the edge, but if he reacts to these then it's a free fsmash/grab/whatever. I can waveland on and either grab, usmash, or roll behind him, but i've been doing that a lot this match and he's probably caught on by now. Lets use upB. I drop from the edge, double jump, and just as my invincibility's running out, I upB straight forward through Marth, hitting him and landing on the stage. He's not facing me, and unless he crouchcancelled it, there isn't really anything he can do before I rising uair and get out of there. The main thing to get right when using this is to get your double jump height just right. If you're too low, you'll upB straight into the stage and grab the edge again. If you're too high, then you'll fall too far after the upB and have a laggy landing.
Also you can occasionally use it semi-offensively while recovering. If you knock someone off stage and jump off to nair them but miss, against some recoveries you can still upB through them and make it to the edge (then continue to edgeguard them). For instance, in a teams match once it was just me left vs a double fox team. I knocked both of them off with a nair, jumped out and dair'd one of them for the kill, then double jumped and upB'd through the other's firefox as he was recovering, making sure my upB still got me back to the ledge. This led to an edgeguard and me looking pretty neato.
You can do some upB ledgecancel stuff too, but Axe would know more about that. Super risky but pretty neato.