A lot of people aren’t quite sure what to make of The Lemon Twigs.

The quartet, led by the D’Addario brothers, Brian and Michael, seemingly went straight from the basement of their Hicksville home into the international spotlight. They raise interest in their unique mix of Beatlesque and Beach Boys’ “Pet Sounds”-era experiments with a wardrobe that looks cobbled together from thrift-store finds and David Bowie’s androgynous years.

“These madcap 4AD signings have become one of the year’s oddest phenomena, their much-praised debut, ‘Do Hollywood,’ resulting in sold-out shows like this,” wrote The Guardian’s Dave Simpson in his review of the band’s show in Leeds earlier this month.

However, the band is quite comfortable being thought of as odd. It’s how they think of themselves. “We lost all hope of fitting into some sort of scene or style,” says Brian D’Addario, calling from a promotional tour stop in Seattle. “We just let everything kind of happen. We just want to make really good songs.”

Both Brian, 19, and Michael, 17, say a lot of their early musical influences came from the record collection of their father, Ronnie, a musician in his own right.

“When we were young, my father started us on ’60s British Invasion stuff, the Beach Boys, The Who and everything rock in the ’70s,” Brian says. “Michael and I moved on to Nirvana later on. We’re always trying to go somewhere different from whatever we were into before. We get a well-rounded view. Now, we end up listening to stuff from Chance the Rapper, Kendrick Lamar and Kanye West. We’ve really gotten into their songs.

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“We used to really hate newer music,” he adds. “But now it’s hit us in a new positive way.”

It’s the combination of new and old, of their youth and love of the past that has helped “Do Hollywood” and its singles “As Long As We’re Together” and “These Words” strike such a chord with those who discover it.

“I been waiting forever to see The Lemon Twigs,” tweeted Questlove, whose early support helped the band make its television debut on “The Tonight Show Starring Jimmy Fallon” in September.

“We just didn’t know what to expect from that show,” Brian recalls. “We were nervous but when it came to the day, everything went great with sound check and what not. It was a huge production and it was so cool.”

But that high-profile appearance was only the start of the admiration for what the band had accomplished.

Boy George tweeted his love of the “As Long As We’re Together” video. French photographer and fashion designer Hedi Slimane dedicated a significant chunk of his influential photo diary to following the band around recently.

And Elton John raved about them on his Beats1 “Rocket Hour” radio show. “They’re so out of left field and I love their songs,” John said, after playing their music. “They don’t have any rules in their songs and that’s sometimes the way it should be.”

He then extended an invitation, saying. “Hey, guys, I’m dying to meet you and keep making great music.”

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The guys were characteristically excited in their tweeted response to Sir Elton: “Yeah boi! Let’s meet up!”

They may soon get their chance. The Lemon Twigs have quickly developed a following in Europe, already playing the famed Bataclan in Paris, as well as a string of sold-out shows in England. The band will launch another American tour that starts on Jan. 18 in Washington, D.C., and ends on Feb. 21 at the Bowery Ballroom in Manhattan, with plans to hit major summer festivals around the world in 2017.

However, while the Lemon Twigs are still in the early days of promotion for “Do Hollywood,” Brian says they are already looking forward to what will come next for them.

“It feels cool to have put out this record,” he says. “But we also feel removed from it at this point. It was 2014 when we wrote the songs and we demoed them that year. We’re kind of anxious to get onto the next one.”