Kieran Culkin is sitting cross-legged on the makeup table in his tiny dressing room. He’s wearing a Marvel T-shirt and is surrounded by little Marvel figurines. “I love ’em,” says Culkin, who is 31 and married. “There’s 50 more under here. They keep falling off.”

He jerks his chin at Michael Cera, his co-star in This Is Our Youth, currently showing at New York’s Cort theatre. “This asshole put his ass on these guys,” he says.

“I was focusing on what I was talking about!” says Cera, known for playing sweet and dorky characters in everything from Juno to Arrested Development. “I didn’t go …” He leaps up and angles his rear at the toys, which have nothing to do with the play they are both starring in. “Oh, you know, that would be fun,” he adds. “I did always want to put my ass on these toys. Can I put my ass on those whenever I want?”

Culkin, younger brother of Macauley, spreads his palms and says: “Dude, feel free, that’s what they’re there for.”

Tavi Gevinson, sitting in the corner and holding a bottle of fruit juice, snorts at this exchange. I get the feeling she is becoming used to the banter of her fellow cast members. A little earlier, in a tone mixing outrage and delight, she said to Culkin: “You burped last night!”

“Oh yeah, that’s right,” he replies, turning to me to explain: “Pretty much any time I go from sitting to standing, I burp. This time, it was a big one. BRRP!”

Although it has yet to officially open, there’s already a sense that This Is Our Youth could be one of the hottest shows of the year, and not just on Broadway. Set in New York in 1982, the play charts two days in the lives of three lost souls. Cera plays Warren, a hesitant, self-searching 19-year-old who has just stolen $15,000 from his rich abusive father. Culkin is his braggadocious drug-dealing friend Dennis, a year older and keen to see the cash put to good use. Dennis was “a dark cult god of high school”, according to Kenneth Lonergan, who wrote the comedy in the 1990s and has watched it become cultishly loved ever since. “[He’s realising] the aggressive hipster techniques with which he has dominated his peers might not stand him in good stead for much longer.”

The play unfolds in Dennis’s apartment: little happens, but plenty is said, every line freighted with emotion. Somehow, the Ronald Reagan references and a plot dependent on a world without mobile phones fail to date it. As the characters strain to become themselves – revealing their needs, aches and humiliations – what emerges is a show that seems perfectly and painfully contemporary. It’s a focused, truthful and vital portrait of what it’s like to be young in 2014, not just 1982.

The night I saw it, a person looking very much like Harvey Weinstein was lurking in the auditorium, one of the few old heads in a very young crowd.

“Oh, you were in last night?” Cera says. “Good. Last night felt good.”

Certainly, I can’t fault Cera or Culkin, but the real revelation is Gevinson – who started out, at the age of 11, as a globally heralded fashion blogger and went on to found Rookie, the website for teenage girls that’s read by every thirtysomething woman I know. She plays Jessica, the watchful, intense fashion student Warren yearns for. In her most recent editor’s letter for Rookie, she wrote about mustering confidence for the play’s first run in Chicago. “I would say out loud – because that’s when things become true – that I am awesome and mighty and cannot be made small.”

Through Rookie, her TED talks and all her other writings about young women, self-esteem and empowerment, Gevinson has become a kind of voice of teenage girlhood. When she offers her take on the play, the other two listen quietly. For all their teasing (Culkin’s impression of her is simply a head tipped back and a groan) they seem to realise that, although she’s just 18, she may be the oldest soul in their trio.

“Being a late teen, done with high school but not an adult yet, is an even weirder in-between than being a teenager,” she says. “It’s equally terrifying and thrilling. When you’re this age, you have no sense of context, or of tomorrow – and it’s really fun to play that on stage. Somehow, through these little events and obstacles in their lives, out comes this really beautiful concentration of all these universal feelings.”

Gevinson remembers how her father, a high-school English teacher, reacted when she got the part. “He was like” – she puts on a dad voice – “‘I think you need to read up on the 80s and get some context for the Reagan stuff and Generation X and how they feel let down blah blah blah.’ I feel like that’s part of it, but it’s not so much a portrait of a period as …” Her voice trails off.

“That’s the thing,” says Culkin. “It’s like, ‘Why now?’ Well, it could be now, it could have been then. Any time would be relevant because of these universal truths. I guess this is my equivalent of a favourite book that I read over and over. I’ve had people make fun of me because I read it, but I’m still laughing at stuff.”

He turns to Gevinson and Cera: “Sometimes when I’m off-stage listening to your dialogue, I still laugh. That’s incredibly rare. Having heard it and read it thousands of times, it can still have that much life in it.”

Cera interjects: “Kenny [Lonergan] will say, ‘This four-line exchange, maybe you thought it was one thing happening, but it’s 10 things.’”

“And then,” says Culkin, “it gets impossible. Here are these 10 things happening in these four seconds and you have to play all 10.”

Some of the lines Gevinson speaks as Jessica could have come straight from Rookie. For example, she tells Warren that the person he is now will bear little resemblance to who he will be in 10 years. “I just know that girl,” she says. “I feel like I know what her Instagram looks like. I think she’s someone who reads Rookie but would be too shy to ever send in her own stuff. I think social media makes people more insecure, but I also think for some girls – like for me – it’s a good way to assert an identity.”

Perhaps the most striking difference between late teenhood in the 80s and now isn’t social media, but drug use. Dennis brags about speedballs, heroin and Dom Perignon, and the play’s most slapstick moment involves Warren spilling an enormous bag of cocaine on the floor, then freezing with horror at the white cloud it throws up. Today’s 19-year-olds seem much more likely to be popping Adderall to stay up all night writing college applications than heedlessly losing themselves in class-As.

“The Adderall culture is relatively new,” Gevinson agrees. “It’s really terrifying.” Nevertheless, she finds herself “amazed at how many people still do coke. It feels really 80s to me. I find it weird when I’m in situations where people are supposedly very hip and they’re doing it. I mean, aside from it being bad for you, it’s funny it’s stood the test of time. But I’m not even in college yet, so I don’t have that much insight into that.”

When her best friend came to see the show in Chicago, Gevinson was dismayed at how quiet she was afterwards. “I was like, ‘Did you not like it?’ And she was like, ‘No, I’m still taking it in.’” It was, says Gevison, the shock of recognition. “So I feel there’s no greater currency in this fuckless planet than when someone can identify with a play, song, band or book. That’s precious, at an age when you feel so lost. When Jessica and Warren connect, it’s like a light at the end of the tunnel. It’s like, ‘Life can be great, there can be these moments.’”

She takes a deep breath. “That’s why I care about this – or anything I do.”

• This Is Our Youth is at the Cort Theatre, New York, until 4 January