Atlus' Persona series has a long history and a very expansive cast of Personas, or demons your protagonist can recruit to their cause. Most of them are based on figures in myth and folklore, along with the occasional historical figure thrown in for flavor. You're given the opportunity to not only bargain with these demons, but also to fuse them together to make even more powerful allies.
You're probably going to be facing off against some very powerful gods and monsters over the course of the game. With that in mind, you're going to need some firepower on your side. Your party can help, but it's your job as a the wild card to acquire the strongest Personas possible and lead your team to victory.
Cybele is the ultimate Persona of the Priestess arcana. Known in the Greek and Roman pantheons as a goddess of motherhood, she can put her nurturing nature to work as a member of your party. Cybele is one of the best healers you can get your hands on.
Her healing skills, like Samarecarm, Mediarehan, and the extremely powerful Salvation—which fully restores the entire party's HP and cures all ailments—are sure to pull your fat out of the fire on more than one occasion. She's weak to nuclear, which becomes more of a problem late game, but she reflects Bless attacks by default and is the only Persona that naturally learns Drain Bless.
Trumpeter is of the Judgement Arcana and is based on one of the seven trumpeting angels that will announce the end times in the Book of Revelation. It can certainly mark the end of your enemies' lives. Trumpeter excels in a support role. It has the auto skills Life Aid, which restores both HP and SP after every battle, and Fortify Spirit, which makes you more resistant to pesky ailments.
Its real power move comes in the form of the debuff Debilitate, which lowers the attack, defense, and agility of one foe for three turns, a great options for boss fights. As a bonus, it isn't weak to anything and sports a number of resistances.
The ultimate Persona of the Tower Arcana represents a Hindu god of drunkenness, with jaws so massive he could swallow the entire universe. He has an unfortunate weakness to Ice damage, but there are ways to circumvent this. On the plus side, he blocks the common late game damage times of Nuclear and Psy, as well as Fire.
He can deal some massive fire damage to enemies and is one of the few Personas that know the Blazing Hell skill. In addition, he provides some passive benefits as well. Unshaken Will makes you immune to mental ailments, and Enduring Soul allows you to survive a single fatal blow and recover all your HP.
7 Black Frost
An evil mirror version of the fun-loving spirit of Jack Frost who, according to in-game lore, remembered its true nature as a demon. It's a powerful member of the Fool Arcana and has no weaknesses, while at the same time blocking, reflecting, or absorbing several kinds of of damage.
It's capable of dealing some very high level Ice damage to foes and has access to the skills Ice Amp and Freeze Boost, making him that much more formidable. You'll probably be a ways into the game before you can recruit him, but it's worth adding him to your team when you've got the chance.
Alice is one of the highest level Personas in the Death Arcana, which might give you an idea of how powerful she is. She's based both on the protagonist from Lewis Carroll's book Alice Adventures in Wonderland, as well as a Scandinavian myth of a child who died and whose spirit gained so much magical energy that it drove her insane.
She's essentially a nuke with a ridiculously high magic stat; she has the insta-kill move Mamudoon as well as Mudo Boost and her signature move, Die for Me!, has a high chance of instantly killing all enemies on the field.
This demon's reputation precedes him. Satan's a prominent figure in Abrahamic religions and is generally depicted as a master of temptation, luring humanity away from God's grace. We don't know what fusing this Persona says about the state of your soul, but he'll definitely be useful on the battlefield.
He has some excellent auto moves that can keep you going for longer, like Regenerate 3 and Invigorate 3, which give you HP and SP after each turn in battle, respectively. It also has access to high level Ice attacks to freeze out your foes, and no weaknesses to boot.
Odin is a representation of the chief god of Norse mythology. He is the father of many other prominent gods and is known for having traded his eye for wisdom. He's a high-level Persona of the Emperor Arcana, reflecting his rule over the Norse pantheon. In-game he's probably one of the most powerful Electric-damage dealers you can acquire, with access to skills like Thunder Reign and Wild Thunder, as well as Elec Amp to really put the hurt on your enemies.
You can boost that damage with the Concentrate buff and don't have to worry about guarding Odin's weaknesses; he doesn't have any. Another of his auto moves, Fast Heal, is really just icing on the cake at that point.
Michael is an archangel in Christian theology, one of the most powerful of God's army, and is also one of the most powerful Personas you can recruit to your team. He has access to loads of powerful damaging moves while at the same time having no weaknesses himself.
He shares Trumpeter's Debilitate skill and can follow up that debuff with his heavy hitters like Cosmic Flare, Megidolaon and the chance to insta-kill with Mahamaon. His most useful and most damaging move is probably Divine Judgement, which halves the remaining HP of a single foe, which can really knock bosses down to size very quickly.
This Persona is almost infamous in the series for being so powerful, almost game-breakingly so. His representation in-game serves as one of the most powerful Personas in the Tower Arcana. He has no weaknesses and is resistant to several types of damage, including the prevalent Physical type.
In addition, his signature move Hassou Tobi allows him to strike all foes with physical damage eight times, which can make even late game boss encounters almost trivial.
Satanael is the ultimate Persona of the protagonist of Persona 5 and can only be unlocked at the very end of the game, at the culmination of the story. He is summoned when the protagonists former Persona, Arsene, breaks its chains and assumes its full power. Satanael can only be fused normally in a New Game+, because of how powerful it is.
It has no weaknesses and in some way resists a whopping ten kinds of damage. You need to be level 95 before you can access him even in NG+ as well as have all the other high-level Personas needed to fuse him, but if power's what you're looking for, you'll find it here.