Pikachu beats Wario. We can combo him with moves like FAir, UTilt, UAir strings, BAir; we're fast enough to avoid the Waft and with our speed, and we can get after him. UAir is a good move here because it juggles Wario and keeps him in the air. Usually when you start to combo as Pikachu, you use up tilt and then use UAir.
Down throw → NAir is not bad here since Wario's frame is big enough to be comboed into NAir after the down throw. Of course you'll have to buffer the dash to go into NAir, but then again, practice is key. I've used this combo against a really good Wario online and can confirm it works (this was lag free on 3DS, btw). NAir is much better as an out of shield option or a "leave me alone" move, but again, it's a decent option after a grab.
BAir is good here. It's fast (frame 4), racks up damage easily, and has priority. BAir's main point is to rack up damage and continue comboing at early percents, so use it for situations like this. You can use BAir to stage spike him too.
DAir is great when SHAC'd and is useful when waiting for the opponent to do something. If they get hit by it in early percents, you can start a combo. Also an okay edgeguard option.
Wario's Neutral B is really good at racking up damage so we don't like getting hit by it. What we could do is not get by it and punish. Bike is good at disrupting our game; his Up B is a good OoS option if it it isn't already, as is his USmash. Try to not land where he can use the latter and just avoid the Bike.
Since Pikachu is a camp-based character, I suggest you camp Wario with Thunder Jolts and down tilts, mixing them up will limit Wario's approaching options. If you do get in, start racking up damage and go back to the camping parade. Rinse and repeat. Speaking of down tilt, use it in neutral. It trips, it gives you a free grab, it has a frame advantage, it's fast. There is no reason to not use this move.
Thunder Jolt is a good edgeguard move both in the air and the ground; the latter being more useful if your opponent doesn't have their second jump. As I said before, this move is good for camping purposes. Wario can get in with his Bike, so be prepared. Don't be spamming Thunder Jolts every time as you'll be predictable.
Waft is Waft. We know what to do: Avoid it. We're fast enough to not get KO'd by it. If we get launched, we can recover with Side B or Up B. The former if you're far, far away.
Quick Attack is our main form of approaching, next to dashing. Wario can approach with Bike, so what we can do here is QA before he uses the Bike.
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KO stuff:
Up smash, forward smash and Thunder are good here. Up smash is good as an OoS option, much like NAir, but at least this one KOs earlier. Forward smash is used for spacing purposes; if you can KO when using it, you're good. Either move is fine, just make sure you don't use them often.
FAir is a good KO method when used near the blast zone. Once you start FAiring, take him to the blast zone to get an early KO.
Now, about Thunder. As always, uthrow → Thunder is a good KO option when the opponent doesn't expect it.
And as for it in the air, yeah... I mean, sure, Wario may use his Bike to help him recover but if you can find an opening in the air, that's where you should use Thunder offstage.
TL;DR: Approach with Quick Attack to start combos, mix up Thunder Jolt and down tilt to camp Wario; avoid the Waft and Bike; KO him once you find an opening. Make sure your grabs are unpredictable so that the Wario player doesn't expect Uthrow → Thunder. Offstage Thunder is good as well. KO options in the ground are usmash, fsmash and.... that's pretty much it.
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I would really appreciate it if someone proved me wrong on this kind of stuff (as in, "correct me if I'm wrong").
This is just what I think about the matchup, so yeah. I usually don't give my opinion regarding matchups because I think I'll be wrong in something.
Wario can eat the Skull Bash and digest the Thunder Jolt faster than Pikachu can make them, but I'm not sure how important this is.
A competent Pikachu player will not be using Skull Bash against Wario. That's just asking for a nice punish by him lol.
The move is only used for recovery purposes.