Advantages:
+Has horrible recovery
+Not much aerial mobility
+Light and floaty
Disadvantages:
-Huge priority on aerials
-Lots of ground mobility
-Plenty of finishers
-Plenty of good defensive options
General Strategy:
This matchup will be all about punishing positional mistakes and knowing exactly when Luigi is and isn't vulnerable, and reacting appropriately. Luigi has huge priority on a lot of his moves and will beat you if you try to contest them. In a game of trading blows he wins easily, but where he struggles is in recovery, his lack of aerial mobility, and his floatiness. This is what have to punish, and fortunately you have tools to do so. Look for openings, get him off the edge, and make sure he doesn't make it back. If you can't accomplish this before he gets to 70-80%ish, upsmash becomes a kill option, if a bit of a risky one.
Approaching:
There won't be much opportunity for traditional approaching against a decent Luigi. With his excellent wavedash he has a lot of ground mobility, which makes it easy for him to wavedash back out of your approach almost regardless of how you angle it, and wavedash back in (if necessary) and punish you. If you ever whiff an approach, he can often dsmash you, short hop into a quick aerial, or occasionally even upB you. He can also beat aerial approaches with fair, dair, or nair, which all have good hitboxes and hurt. His fireballs are pretty bad, so you don't have to worry much at all about them while approaching, you just have to worry about the wall of priority he can quickly create around him and his slippiness on the ground.
This doesn't, however, give him free reign to just sit and throw out moves. His aerials have good priority, but there's also a bit of lag after them. His wavedash is really good, but there's still a short interval at the start of it where he can't do anything. He also can't cover a lot of distance with wavedash if he runs out of platform/stage room in the direction he wants to go. There are holes in his defense that you need to bring out and take advantage of. Fakeing approaches can be pretty valueable in this matchup, as causing him to whiff something opens up small options for you. For instance, if you jump forward and then waveland back before you reach him and he falls for it expecting you to commit to the approach, he'll likely do one of two things as mentioned before. If he wavedashes back, then you remain out of lag and far enough away that he can't punish you, but now you've pushed him closer to the edge so he has less room to work with. If he jumps and throws out an aerial, then you can either punish the lag of that aerial with a nair if you're close enough, or just move close enough that he feels threatened. If he's in the air and you're out of range of his fair and dair, then there isn't much he can do to you from that position because of his lack of aerial mobility, while you threaten to jump forward and immediately nair, or usmash him before he lands, at any point. If he does nothing or throws out a defensive aerial before you do anything, you get a free punish on that. If he then double jumps to reposition himself, you can uair spike him. Off the stage without his double jump is a dead Luigi.
Combos:
Comboing Luigi is difficult to impossible because of how fast his nair comes out and how it beats almost everything. For this and other reasons, you want to end combos pretty early and safely on him and try to end the combo with something that will send him close to or off the edge of the stage. You want to gimp him, building up damage on him is secondary. He's pretty light and floaty as well, so simple uair->nair or uair->uairspike combos are about as much as you'll get.
Killing:
Gimp him. Force him towards the edge by getting him into the air, finding holes in his defense as outlined before, and then knocking him towards the edge with a nair or uair. Throwing out fsmash is also pretty safe as long as you don't completely whiff. It has good range, will beat him if he tries to wavedash in and do something, and most importantly has the knockback to send him off the stage at low-mid percentages. If he shields it, it also has the shieldstun and will push him back far enough that he can't really punish it. Your main priority is to get him off the stage, pretty much regardless of what his percentage is, and then edgeguarding him which should relatively easy.
KOs off the top are still possible once he hits 70%ish on most stages Due to his ground mobility, having a usmash whiff or get shielded lets him get free damage on you, and kill if you're at higher percentages. Use it sparingly and don't make it obvious that you're going for it, but use it if the opportunity presents itself. It's pretty much always ok to trade usmash with one of his aerials, it will trade.
Edgeguarding:
Luigi's recovery can be a bit awkward, but it's pretty bad and punishable. First off, you need to understand his recovery options. He's floaty, so he can get some distance from just holding forward as he falls. He can also forwardB, which gives him a little distance. 1/7th of the time this will misfire, giving him a lot more distance and speed as well as a lot of knockback if he hits you. Watch out for this, but it's generally easy to counter (while powerful, its hitbox isn't that good and can be cleanly beaten by just an ftilt, or you can shield it and punish its lag) if you anticipate it. He has an alright second jump that mostly gives him vertical distance, and he also has one downB which turns him into a hitbox and gives him a small amount of vertical and horizontal distance (but mostly just stalls his recovery). Lastly, his upB goes only vertically, making it generally easy to edgehog. Because each of his options are relatively short and linear, it means it can be very difficult to recover if he's sent below the stage at a diagonal angle from the ledge. Which is exactly where uair spike will put him.
For general edgeguarding, get a good understanding of what his recovery options are, wait for him to commit to one, and then try to punish that. If he overBs from too high/too close to you, you can easily uair spike it (as long as it doesn't misfire). If he tries to get under the stage and recover from directly below, you can edgehog (normally, or with a surprise upB ledgehog from the stage) relatively easily. Just watch out for him to delay his upB by downBing first and wear out your ledge invulnerability or bait you into rolling onto the stage too early. Jolts can be useful for catching him off the stage, but due to his floatiness he'll usually just use them to get a little height and then forwardB again hoping to misfire. Generally it's best to chase him off the stage yourself.
What to watch out for:
The main things to watch out for in this matchup are his aerials and his wavedash. In the air, his moves beat yours. If you can get under him, your uair will still go through anything he has and due to his floatiness he can't easilly fastfall onto you with something, but from about any other angle his aerials win. Don't try to contest them unless the reward greatly outweighs the risk (i.e. you're at very low percent, are pretty sure you can trade your dair with his whatever, and you know it will kill him). His wavedash is also pretty scary, as it allows him to cover a lot of ground quickly and he has decent options out of it. Wd into ftilt covers a huge area and can put good pressure on you. Wd into dmash is pretty quick and does good damage, while wd into fsmash is a little delayed and can catch you if you're expecting ftilt/dsmash, and also does good damage. He can also grab you if you try to shield as he comes in, which leads to usually dthrow->aerial.
Recovering:
Recovering against Luigi isn't too bad as long as you don't make any huge mistakes. If he kills you it will generally be from the sheer knockback of his moves, rather than from edgeguarding. He can't really chase you off the edge due to his poor recovery, fireballs are awful for edgeguarding, and the only things he has that reach below the ledge are aerials. Just remember that if he's on the stage, he can wavedash to the ledge pretty quickly from a good distance. If he's ledgehogging, he can wavedash a good distance onto the stage and catch you if you try to recover there. It's generally pretty safe recovering to platforms, the most he'll get on you is usually an aerial that you can DI and stay on/near stage at low-mid percents (which is better than losing a stock to edgeguarding).
Final Notes:
Take him to the air where he's least mobile, use your mobility to fake approaches (and keep him on his toes with occasional real approaches) and force him to commit to options, and then use these created openings to push him off the stage. Uair makes this matchup doable for you, I can't stress its importance enough. Use your aerial mobility to keep the momentum on your side, as if you let him set up his game then you'll find yourself with increasingly less space from his wall of aerials and quick ground approaches. If he does get in on you, try to get to the air and escape to platforms until you're in a better position to move around and create openings yourself. Be mindful of his nair, as it can quickly turn momentum in his favor. Don't get greedy with combos, just do a couple of hits and try to force him towards the edge, racking up damage is secondary. Focus on gimping him and respect his aerial priority, and you make this matchup that much easier.
Stage Counterpicks:
Dreamland, Pokemon Stadium, and Fountain of Dreams are all decent counterpicks against Luigi in my opinion. Dreamland is big, which gives each of you decent room to move around, but the large blastzones extend Pikachu's life noticably while not doing much for Luigi. Pokemon Stadium allows for earlier usmash kills, and also the transformations tend to favor Pikachu more than Luigi. Fountain of Dreams is a little risky, as Pikachu will die sooner, but the unique slidiness of the stage makes it easy for many moves to push Luigi towards the edge on hit or shield.