Until recent events at the Oscars, the film season’s most memorable best actor speech belonged to Caleb Landry Jones. In July, the Cannes Film Festival awarded Jones its top male thespian prize for his portrayal of a mass shooter in the Australian drama “Nitram” (now in theaters and on digital). The 32-year-old actor had been to Cannes twice before and had experienced its queasy jitters, spurred by drinking too much, sleeping too little and feeling eyeballs scan his face to gauge his importance. (“L.A., but times 50,” he said.) But this time, all eyeballs were fixed on him as he clutched the awards podium like a fainting chaise. “I think I’m going to throw up,” he sputtered. The audience tittered, uncertain if his panic was a bit. Then Jones fled the stage, leaving in his wake a few exhalations that lingered like dust clouds from a cartoon roadrunner: “I am so sorry — I cannot do this. Thank you so much.”

“I wanted to be invisible,” Jones recalled. “I was barely forming words, and I thought, ‘I’ve got to give up.’” Re-enacting the moment, he bellows, “Caleb Landry Jooooones,” seal claps and then pantomimes his flailing heebie-jeebies.

The Texas-born actor who still speaks in a singsong twang looked exponentially more relaxed the day we spoke in the backyard of his 101-year-old ramshackle rental house in Los Angeles. In a corner of the city that doesn’t yet have a gentrified name, the people around him (mostly) don’t mind if he plays guitar at 2 a.m., or if he and his girlfriend, the artist Katya Zvereva, set out paper plates of tuna for the stray cats. Here, it’s OK if Jones steels himself for stress by rolling joint after joint in the sunshine, as he did during our talk. Later that afternoon, he was headed to the dentist for four root canals. “That’s why I’m getting as loaded up before I go in as I can.”

“Invisible” isn’t a word often applied to Jones. The redheaded actor has been a distinct onscreen presence ever since he landed his very first screen audition at 16 for a one-scene role in the Coen brothers’ “No Country for Old Men,” as the boy who biked up to a bloodied Anton Chigurh (Javier Bardem) and delivered the memorable line, “Mister, you got a bone sticking out of your arm.” Jones roiled with menace as the racist son in Jordan Peele’s “Get Out”; riddled his skin with diseases in Brandon Cronenberg’s bio-horror “Antiviral”; and set himself on fire in the Safdie brothers’ “Heaven Knows What.” For most of his career, he’s favored vibrant bit parts for prestige directors — Jim Jarmusch, Sean Baker, Martin McDonagh, Lone Scherfig, David Lynch — over lesser films that offer more screen time.

Jones is an odd strain of rebel — not a slick James Dean clone, but a cowlick that can’t help doing its own thing. He’s at once meticulous and sloppy. After a childhood diagnosis of obsessive compulsive disorder, he became conscious of the need to invite entropy into his life. At his home, while his brain whirred with specifics — did he put exactly two teaspoons of red pepper in last night’s chimichurri? — he projected disarray: paint smeared on pants, rumpled sweater, scruffy goatee. (He certainly didn’t seem to have packed a comb for his scraggly locks at Cannes.)

Zvereva, who came outside during the interview to offer us more coffee, said that when Jones first approached her on the street in New York, she thought he was homeless, even after she invited him to her studio and he, in turn, walked her to his film set, where his director cried happily that Jones had found another person on his wavelength.

Growing up just outside of Dallas, Jones was encouraged to follow his creativity. His parents, a special-education teacher and a contractor, allowed him to draw all over the home’s floors until the plywood was replaced by hardwood planks. His mother enrolled him in ballet and tap, prodded him to audition for the local arts magnet, and served tea and graham crackers alongside hours of British comedies — “Monty Python” and “Wallace and Gromit,” and deeper cuts like “Only Fools and Horses.”

A church kid, he wasn’t allowed to read X-Men comics, and he didn’t until he played Banshee in “X-Men: First Class.” Though he loves music — and, in fact, just released his second album of warbly psychedelia — as a lanky teenager, Jones waved off Nirvana for the Christian band DC Talk (he once saw them open for Billy Graham). That was until he got fixated on Bob Dylan and emulated his new idol by shrinking his shoulders and wearing tight pants.

“Stuff affected me too much,” Jones said. Each new obsession, like Radiohead and Bukowski, has had a way of temporarily overtaking his artistic temperament. “That’s why it’s good to find acting,” he added. Exploring a character — especially a cryptic one whose choices defy expectations — gives him the language to grapple with his own desires.

“He’s the most immersive actor I’ve ever worked with,” the director of “Nitram,” Justin Kurzel, said via Zoom. “He’s a real artist.” Even though it’s difficult to tell Jones so to his face. “Whenever you praise Caleb, I can see he’s uncomfortable.” Their film is inspired by the 1996 mass shooting in Port Arthur, Tasmania, which motivated the Australian government to pass the National Firearms Agreement prohibiting automatic and semiautomatic weapons. It dominated the Australian Academy of Cinema and Television Arts Awards in December and earned Jones a second best actor statuette. (This time, he was able to prerecord his speech.)

His character — only referred to as Nitram, so as not to lionize the actual shooter, who remains in prison — plods through the movie like an intimidatingly oversized child. He rages and sulks; he suffers feeling rejected for reasons he can’t always control. And, at the end of the film, he finds one community who welcomes him (and his money): gun shops, who play nice to the visibly unstable man and sell him whatever rifles he wants.

Jones, who had been asked to waste away over the duration of the Australian shoot, chose to secretly gorge on meat pies so that he’d take up more space. “No, we’re going ‘Fat Baby Man!’” he said, chuckling. Much of the film was improvised. They’d play a scene loud, and then try it quiet. To understand the gap between how Nitram saw himself versus how others perceived the inarticulate, angry young man, Kurzel assigned Jones tasks: film himself with a video camera, doodle in a diary. “I’d draw myself with muscles, and I’d write ‘sexy’ next to it,” Jones said.

“I’m not sure if I really did ever meet Caleb,” his “Nitram” co-star Judy Davis said by phone. “He was always using an Australian accent.” During their punishing scenes as mother and son, Davis, herself an award-laden screen veteran, admired Jones’s openness and lack of pretension. “Probably the most responsive actor I’ve ever worked with.” When not on set, she tried to trap him into accidentally using his real voice. Only on her last day, before the end of filming, did Jones startle her by breaking character to run up for a goodbye hug.

As the shoot approached its final explosion of violence, which Kurzel chose to keep offscreen, Jones became increasingly withdrawn. The local crew, painfully familiar with the actual tragedy, began to keep their distance from Jones, particularly after the guns arrived on set. “I wasn’t finding as many friends,” Jones said.

It may sound agonizing for an artist to feel so alone halfway around the globe from home while handling such intense material.

“But it’s great!” Jones insisted. “It was really wonderful for me because I don’t know how to act.” Maybe he should let his awards have the last word.