1) Head-butt
Next to the phantom uppercut, this is by far Luigi's most powerful launcher. The difference between the head-butt and the phantom uppercut, the fact that puts the head-butt at the top of this list and the phantom uppercut at the bottom, is that it's actually very easy to connect with the head-butt. As soon as anyone even gets near Luigi from above or even from the sides, unleash the headbutt and you'll probably connect and your opponent will probably be KO'ed.
2) One-spin throw
Not a very powerful throw but it gets the job done as most throws do. Not very vertical so your opponent won't have an easy time getting back plus, as with almost every throw, the setup time and recovery time is almost non-existent.
3) Multi-spin throw
This throw might actually be a little bit weaker, or stronger than the one-spin throw. We really can't tell just yet. And, while this throw will hit other opponents as Luigi spins his opponent around, you're probably going to be fighting offensively while facing an edge and defensively when facing away from an edge. Therefore, you'll probably use the one-spin throw much more for launching and that's why it has a higher placement than the multi-spin throw, because it fits the situation much better.
4) Strong punch
This is a very good horizontal launcher that also has a good horizontal range considering Luigi takes a step before punching and then his fist "grows" when he hits with it. The reason that this move isn't better is just that Luigi takes that first step which is definitely a setup. Therefore, if someone is running at you, there's a good possibility that you're not going to get the attack off before they get theirs off.
5) Sweep on both sides
Not very powerful but it doesn't launch your opponents very high. Therefore, if you get someone near an edge, they won't have a great opportunity at getting back to the platform. It also great range as Luigi will hit characters in back of and in front of him. However, he doesn't do them at the same time, he hits first back then forward and so he has setup and recovery time on the move.
6) Backwards kick
Another move that really isn't all that powerful. And, the bigger problem with it is that it's very hard to connect with. You have to be facing away from your opponent in the air to connect with it and basically, there aren't going to be very many times when you want to be in that position.
7) In-air phantom uppercut
We'll tell you, the phantom uppercut has to be one of the most annoying moves in Super Smash Brothers. If you are not exactly next to an opponent when you use it, it won't be a phantom uppercut but a coin uppercut. But not a coin uppercut like Mario's multiple-hit coin uppercut. You'll only get one hit and your opponent won't exactly bounce into the air. It's so easy to miss and so easy for your opponent to counter when you miss.
8) Phantom uppercut
At least when you're in the air you can try to get close to your opponents to use this move. At least there is some kind of range involved there. Perhaps, just perhaps, if you can master the timing and range, you'll be able to pull this move off after an opponent comes back from a launch and is landing after an Up + B move. But I wouldn't be betting on it.