In Marvel comics, many of the superhero teams made up of mutants don't just save the world together; they live together, and sometimes, attend school together as well. That's especially true for the mutants who begin to understand their abilities under the tutelage of Professor Charles Xavier.
In the case of the New Mutants, the teenagers are brought together as a younger generation that are never meant to go out into the field like the X-Men. They are supposed to live and learn together without the pressure of becoming superheroes. That didn't exactly work out as the teenagers quickly begin using their abilities to save the day. Their school set up isn't exactly Hogwarts, but if it was, these would be their assigned houses.
Cannonball: Hufflepuff
Sam Guthrie is a young man from Kentucky who just wants to do the right thing. When his father dies, he supports his family by working in coal mines - even though he shouldn't even be old enough to do that. When his power manifests while and a coworker are trapped underground, allowing him to blast them through the mine to save them, he gets hired by the Hellfire Club, but Sam doesn't know what he's in for.
Loyalty and responsibility mean everything to him. When he realizes just what it is the Hellfire Club is asking him (to kill teen mutants), he leaves. Cannonball spends most of his years trying to help those who need it, and he never turns his back on a friend. Loyalty as the root of his motivation makes him a lock for Hufflepuff.
Magma: Gryffindor
Like many of the later additions to the New Mutants team in the comics, Amara doesn't make it into the new movie, but she's a big presence in the comics. Amara runs just as hot as the lava she can control.
She's always ready to jump right into a fight. Long before she ever meets the rest of the New Mutants, she's already trying to do the right thing for her people, going undercover amongst villains to help save the day. Her bravery and willingness to give her all in a fight make her an easy sort into Gryffindor.
Wolfsbane: Ravenclaw
Rahne Sinclair is aged up just a bit for the movie as she's only 13 when introduced in the comics. Her ability to turn into a wolf makes her a target of the conservative people around her, who don't understand she's a mutant.
Because of her faith, Rahne has a hard time understanding the changes happening to her at first. She's a bit of an overthinker, examining a situation from every angle before making a decision. That also tends to make her a bit philosophical, and a great fit for Ravenclaw.
Karma: Hufflepuff
This founding member doesn't make it into the New Mutants movie, though she would have been in sequels had they been made before the FOX-Disney merger. Xi'an Coy Manh is one of the few New Mutants recruited before the team is formed. She has custody of her younger siblings, and needing a job when they make the move to New York, she agrees to work for Professor Xavier after he helps her out of a jam.
Shan, as the team nicknames her, always finds herself pulled in a million different directions. She's one of the hardest working members of the team, splitting her time between honing her gifts, raising her siblings, working for the professor, and supporting her friends. Hufflepuff would welcome her into the fold.
Sunspot: Slytherin
Roberto da Costa (Sunspot) has traits from a lot of the Hogwarts houses. He's as hardworking as a Hufflepuff, as brave as a Gryffindor, and as intelligent as a Ravenclaw. Ultimately, however, it's the ambition and cunning of Slytherin that would win out.
As he grows up, Roberto not only takes over the family business, but he uses his family connection and money to turn other, more sinister, enterprises to the side of good. Roberto uses his own ambition and prowess in the business world to make a difference.
Cypher: Ravenclaw
Doug Ramsey is initially not a member of the team, but instead a friend of Kitty Pryde's at Xavier's school. His ability to communicate in any language, however, makes him a pretty valuable addition.
Those communication skills aren't what get him sorted into Ravenclaw. Instead, it's his technical prowess. Doug has a deep love for technology - especially video games. He learns everything he can about new pieces of technology, putting his skills to use, and even writing his own software.
Magik: Slytherin
Illyana Rasputin spends a lot of her formative years fighting the darkness in her thanks to years spent learning sorcery in Limbo. Despite her often believing she's a bad person, she's a hero.
Illyana's story in the New Mutants movie is more comic book inspired than it is comic book accurate, but she's still got the same caustic wit and knack for getting her friends into trouble. She can be manipulative - whether it's getting a teammate to spill a secret on screen or getting her brother to harness a dark power on the page. She's definitely a Slytherin.
Rictor: Gryffindor
Julio Richter begins his journey with the New Mutants as the prisoner of a villain. His power is exploited before the team can save him and take him under their wing. Despite everything he's already been through, and the emotional trauma he experiences throughout the comics, he still trains to be a superhero.
Of course, Rictor does tend to be a bit impulsive. His tendency to jump to conclusions quickly, and rebel against the leaders who have his best interests at heart, scream Gryffindor. Gryffindors tend to follow their hearts moreso than their heads, which can lead to some impulsive behavior.
Mirage: Ravenclaw
Dani Moonstar is one of the first of the New Mutants team in the comics and on screen. Her abilities allow her to manifest people's darkest fears or deepest wishes, which can make for an interesting weapon against an enemy in battle.
Dani grows into someone who has nearly perfect control over her powers - and she grows her powers significantly over the course of her time in comics. She has to come up with creative ways to use her ability. As an adult, she even becomes a mentor for young mutants learning to control their own powers, as well as an American History teacher. Her ability to take in and digest information the way she does makes her a good fit for Ravenclaw.
Warlock: Hufflepuff
Often mistakenly identified as a robot, Warlock is a techno-organic alien who can shapeshift. He was a planned inclusion when the characters came to the big screen, but didn't make the cut. Unlike most of his race, he has no interest in infecting living beings with the virus their race is known for. His compassion makes him standout, and leads him into allying with the New Mutants.
That compassion, and Warlock's desire to help instead of harm, makes him a great candidate for Hufflepuff. His compassion also created a protective instinct in him, leading him to put himself in the line of fire for his friends numerous times.