Tilda Swinton has always exuded an otherworldly aura. Maybe it’s the pale, almost translucent skin that highlights her steely blue eyes. She speaks with such rabid intelligence that even a casual conversation sounds like it was scripted by Dorothy Parker. She seems impossibly tall, a willowy figure whose striking, androgynous looks have been tilted toward a wide range of menacing characters.

In Wes Anderson’s latest fairy tale, “The Grand Budapest Hotel,” the 53-year-old Scottish actress is virtually unrecognizable under droopy skin and wrinkles as octogenarian Madame D. In the just-released drama “Only Lovers Left Alive,” directed by Jim Jarmusch, she portrays Eve, a chic-looking (if 3,000-year-old) vampire. And in June, she’ll be seen Stateside in Bong Joon-ho’s futuristic “Snowpiercer” as a terrifying political leader whose inspiration draws from equal parts Kim Jong-un and Marilyn Manson.

Her versatility as an artist makes her impossible to classify.

Along with a prolific screen career highlighted by an Oscar win in 2008 for her portrayal of an unraveling lawyer in “Michael Clayton,” Swinton also performs spoken-word pieces, has founded a film festival (Scotland’s Ballerina Ballroom Cinema of Dreams in 2008), and inspired a collection from Chanel.

Her best-known work might be “The Maybe,” a live performance-art piece in which she sleeps inside a glass box wearing nondescript clothes and muddy sneakers, which she has been staging for 19 years in galleries and art museums around the globe, including MoMa in New York.

“Tilda is an artist, an activist, a film historian, an instigator and a writer,” says Jarmusch, who has collaborated with the actress on three movies. “What isn’t she? There is nothing she can’t do, nothing she can’t play.”

Though she spent the first nine years of her career making experimental films with mentor Derek Jarman, Swinton has occasionally branched out into more mainstream Hollywood fare, portraying the evil White Witch in “The Chronicles of Narnia: The Lion, the Witch and the Wardrobe” and a surreal saleswoman in Cameron Crowe’s 2001 thriller “Vanilla Sky.” She’s essayed everything from a nobleman who switches genders in “Orlando” to the archangel Gabriel in “Constantine.” Directors including the Coen brothers and Spike Jonze have lined up to work with her.

Yet Swinton says she doesn’t consider herself an actor. “I don’t know what it would take for me to feel like one,” she says. “I understand it’s a strange thing to say because I do keep saying, ‘Yes, I’ll dress up and be in your film.’ But when I hear proper actors talking about their lives and how they approach their work, I feel like I’m up another tree.”

Swinton doesn’t lead an actor’s life. She spends most of her time in the Highlands of Scotland, far from the lights of Hollywood. She claims to not know how to talk about her craft. “When people ask about how I approach a character — well, I wouldn’t know how to approach a character if I tried,” she says. “People will ask about choosing a role; I don’t choose roles. People will talk to me about preparation. Aside from putting together a disguise, I’m not aware of any preparation at all.”

Swinton is the first to acknowledge she didn’t grow up immersed in movies. She was born in England, daughter of Maj.-Gen. Sir John Swinton, the former head of the Queen’s Household Division — the men on guard at Buckingham Palace. She attended several boarding schools, including West Heath, where she was a classmate of Diana Spencer, who one day would become Princess Diana. While attending Cambridge U., where she planned to focus on writing, Swinton began to get involved in plays. But still, she says, “I had a very ambivalent relationship with the theater.”

She did audition for and get accepted into the prestigious Royal Shakespeare Company. “It was after a year there that I decided I didn’t want to be an actor,” she says. “Which was a really good piece of information to have. It’s a good thing when you’re a young person to find out what you don’t want to do.”

But shortly after leaving the RSC, she was introduced to Jarman, an English film director and stage designer, through mutual friends. “He met me at a door with a videocamera and we started talking, and we never stopped,” recalls Swinton. The two became fast friends and would, over the course of eight years, collaborate on seven features, beginning with 1986’s “Caravaggio.” Swinton has said it was Jarman’s death in 1994 from AIDS that was the impetus for “The Maybe,” since she wasn’t sure she’d continue making films, and wanted to find “a gesture” between live performance and what she loved about working onscreen.

The association with Jarman set the tone for a career that hasn’t followed the route of the typical actor. “Most people don’t develop work the way I customarily do,” she notes. “They’ll wait for someone to place them into their universe with proper crafts­people. Whereas I spend most of my time sitting around my kitchen table with friends, chewing on ideas and building things that take years.”

She spent five years with director Sally Potter on 1992’s “Orlando,” adapting Virginia Woolf’s story of an eternally youthful nobleman who at one point changes gender. After so much time developing the project, Swinton concedes there was one drawback: She hated the movie at first. “Because it was like a trailer for my fantasies,” she explains. “You work on something for five years, you fantasize it will be five hours long and occupy all your wildest dreams. Then it goes by in 90 minutes. I love the film now, but it took me a long time to appreciate it.”

Swinton has learned to separate the experience from the final product; a healthy perspective, as she regularly spends years working on a picture. In the case of Luca Guadagnino’s Italian romance “I Am Love,” it was 11 years.

“Only Lovers Left Alive” — which Swinton refers to as “only” taking seven or eight years — began with a phone call from Jarmusch suggesting they make a vampire film. It seems such obvious casting it’s hard to believe the actress has never played a bloodsucker before. “She’s such an exquisite creature on so many levels, and physically so beautiful and graceful and striking and pale and, yes, vampire-like in a lot of ways,” Jarmusch reasons.

The director says Swinton was so central to the project that the two of them worked together on every minute detail, including costume, movement and dialogue. When Jarmusch felt the vampire wigs in the film didn’t look wild enough, it was Swinton who suggested using animal hair. They ended up making wigs from human hair mixed with yak and goat fur. “She has little insights constantly. She’s one of those people so obsessed with what she doesn’t know. Rather than spewing out all the things she does know, she wants to learn something new that will amaze us all.”

Jarmusch even asked Swinton to write certain scenes. He was so taken by her State of Cinema essay presented in 2006 at the San Francisco Film Festival that he asked to use phrases from it in their second film together, 2009’s “The Limits of Control.” In “Only Lovers Left Alive,” he had both Swinton and co-star Tom Hiddleston write their dialogue for a fight scene. “These words are from Tilda, when she says, ‘This self-obsession is a waste of living that could be spent on surviving things, appreciating nature, nurturing kindness and friendship and dancing.’ ” Hiddleston has fond memories of working with his co-star: “She is so generous with her curiosity that when we were in prep, we would disappear down rabbit holes together, talking about poetry and music and history and art.” The actor said the two danced together, “mostly to the kind of Memphis soul or Detroit Motown you hear in the film.”

When Swinton met Bong at the 2011 Cannes Film Festival, and he spoke to her about “Snowpiercer,” she insisted there wasn’t a part for her. The director told her not to worry, and they soon began talking about building the character of Mason, who is described in the script as “a mild-mannered man in a suit.” Says Bong, “My team and I didn’t think twice before changing Mason into a female character — or, actually, a character that transcends gender.”

Bong, too, says Swinton was integral to building the role, adding that Mason’s unusual appearance was entirely her idea. “She is always filled with the desire to transform herself and create something new,” he says. “We experimented to the point that Tilda was virtually unrecognizable — dentures, prosthetic nose, thick-rimmed glasses, wigs, everything. Even under such heavy makeup and costume, she performed with such fluidity and grace, and I was constantly amazed.”

Swinton has never auditioned for a role — unless you count a casual meeting with the Coen brothers for “Burn After Reading” in which she has a vague memory of running some pages. Filmmakers, such as Wes Anderson, who first became aware of her at Sundance in 1993 (she was there with “Orlando”; he had the short film “Bottle Rocket”), seek her out. A self-professed fan, Anderson first hired Swinton as the aptly named Social Services in “Moonrise Kingdom,” before casting her in “Budapest.”

“I would use any excuse to try to seduce Tilda into one of these movies, but I particularly thought she might like the opportunity to age very suddenly,” Anderson explains of offering her the role of Madame D. “There is a sort of concept-art aspect to it. Tilda, as we know, is not just a magnificent actress, she is also a sort of visual performance artist at large in the world.”

As for future projects, Swinton says there are a few things she’s “chewing on.” She will likely reprise “The Maybe” at some point, though she notes: “The idea is that ‘The Maybe’ is ongoing. It’s scheduled, but there is no schedule.” For now, she’s happy to return to Scotland with her twins, 16-year-old Xavier and Honor; and boyfriend, artist Sandro Kopp. Their relationship has been the center of some media attention: Kopp is 17 years her junior, and some outlets reported she had an open relationship with John Byrne, her longtime partner and father of her children.

Swinton says she and Byrne were no longer together before she became involved with Kopp, and she never felt compelled to clarify it to the press. “We didn’t realize for about three years there were these myths that everybody was living together in some kind of a cabal,” she says with a laugh. “It’s all rubbish, and nobody’s getting hurt along the way.”

Indeed, Swinton takes neither her personal nor her professional life too seriously. “I’m playful at heart,” she says. “And myth-making is always fun.”