Lumina was designed to combat Junko's Despair, thusly, her "special power" is being AI and being able to hack into, and live in, any electronic device or screen.
Michiru's Talent was inspired by her role in All Mix, often an announcer for the events happening in the show. Her power is a projected voice that can be strong enough to be a mini "sonic" weapon.
Since I have yet to think of a good Talent for Kokoa, she's a ?
As for Hayate, as a poet, she's excellent with words and so can charm almost anyone with anything she says, no matter how nonsensical (so canon Hayate).
Neo's pretty self-explanatory, but she's hoping (ha ha) to one day be the Ultimate Diva. To her, it sounds more powerful, and because it's rarer than Ult. Vocalist, she perceives it as superior. Her power is vocal hypnosis, so similar to Hayate, but not the same, as Neo's voice can put people into trances. Hayate can just convince people to do just about anything she wants, if she tries hard enough.
Sophia, as an empath, is literally able to sense and feel the emotions of others. Her "wolf senses". She can also be a lie detector, but she has somewhat nuked herself because of her low esteem and obsession with Neo. Neo is the only person she cares to use her empathy to read and understand.
Elsie's Talent came from her father and the family wealth and power. She could've also been Ult. Mafia the way Fuyuhiko is Ult. Yakuza.
Weronika's Bear Paw attack is so powerful that it actually is as strong as a full-grown, healthy, fit, angry grizzly.
Because I'm Abyssmare obsessed, I made them extra cards.
I headcanon that if these guys were in a Killing Game, Sophia would be introduced as a reserve course while Elsie would be introduced as the Ult. Mafia Leader (later revealed to be false, she's coming in as the Ult. Sponsor, inspired by her father).
But then, at the end of the game, it's revealed that Sophia actually IS an Ultimate (and a powerful one at that, because of what her extreme empathy and senses can tell her about other people) while Elsie is the reserve course. She just tried to pay her way in, explaining the two other Talents she claimed she had.
Then Weronika's real Talent is related to her looking after her 3 younger siblings, but of course she doesn't want to admit that.
Meanwhile, Neo gets nothing because she's such an OP prodigy in the game that it amuses me to think that she's the only one of the quartet whose Talent isn't buried behind lies.
Just a funny bonus, Hayate Tendo is the Ult. Lesbian. Yes, I know they're both gay, but Hayate is way smoother. Kokoa is a baby gay, LOL.
With this Talent, she has the ability to woo any woman she wants, though it's debatable how in control/intentional she is with that power (as an illusion to her strange, eccentric, effortless charm in canon LOL)
AN: BTW, check out the fanfic "Danganronpa/D4DJ One-Shots" by Irhaboggler if you want to see character interactions and how the class trials and video game elements would work!