There are certain things, says Ezra Furman, that people expect of you when you become reasonably well known. In his case, it is that he will turn up to photoshoots and gigs wearing a dress and make-up. That's what happens when you describe yourself, as he did once in an interview, as "gender-fluid".

"I've shown up at shows, and people have been, like, 'Why aren't you wearing a dress?'. I took photos for a magazine, and they were like, 'Well, you have to wear a dress. You have to wear make-up, because that's what we thought you wear and that's what the idea was for the photo.' That's not what fluidity means," he chuckles, on the phone from San Francisco. "But y'know, it's fine. I'm more excited about just being visibly queer, y'know? Being visibly gender non-conforming. We need a lot more visibility of queer people in public life. People gotta get used to it."

The 29-year-old Chicago native can laugh about it, primarily because he is the sort of musician who enjoys confounding expectations - whether it’s through his fluctuating dress sense or his remarkable songs. There is nothing of the “show off” in Furman’s nature, though; you get the impression from his slightly awkward conversation, filled with a degree of goofiness, long pauses and thoughtful answers, that he is the sort of musician who lives his art. Career trajectory doesn’t seem to be a priority; he is as open about his lack of adherence to societal norms as he is about his devout Jewish faith (until last year, he refused to play gigs on Friday nights in observance of the Shabbat).

It’s not necessarily the sort of kid that you can imagine falling in love with the Sex Pistols at 13, but that’s the passage that he took into the world of music. “I heard the Velvet Underground and that changed things when I was like, 15. Before that, the first gateway in was Green Day and then from that to other punk bands, like The Ramones and the Sex Pistols. After that, I was obsessed with trying to figure out what it was to be a great songwriter.”

He kick-started his experiments as a teen, taking his cue from Bob Dylan songbooks that his mother gave to him. Later, he progressed to public performances by playing open mic nights in Chicago.

“Then I started to realise how boring they are. It’s just like a bunch of people playing really boring things, and closing their eyes and getting really passionate and communicating nothing. It was like, ‘What if I started a song with this line? That would wake everybody up, and they might think, Hey, this 15-year-old kid is actually saying something.”

Furman’s knack of catching the listener with a sucker-punch of a lyric before reeling them in with catchy melodies has become his modus operandi. There is a sense of the surreal in some of his songs; others are steeped in the perennial self-deprecating outsider wit that songwriters like Stephin Merritt and Morrissey have made their own.

“They’re my heroes,” he says, unsurprisingly. “They were my early awakening, a realisation that I could do it. They had something unexpected. I could write a joke song really easily, but I think something that might be true for my generation is that there’s a certain irony or detachedness expected of us, even though we really feel sincere. So the only way to sincerity is through a joke. There’s some kind of barrier to get through before you can say ‘I love you’ or ‘I’m hurt’ if you haven’t first pierced this cultural shell in some way.”

Musically, his most recent brace of albums – 2013's Day of the Dog and this year's Perpetual Motion People – have elicited comparisons with everyone from Jonathan Richman to Lou Reed to Elvis Costello. On the latter, in particular, there is a heady concoction of everything from 1960s rock 'n' roll to doo-wop, new wave, contemporary indie-rock and even a country-folk song, as well as lyrics about his sexuality and the state of the roads in Chicago. .

There is a typically droll line on the album track Watch You Go By that runs "I've got a bright future in music, as long as I never find true happiness", but it's an old one. "I reject that line utterly," he now says, laughing. "It was a bitter joke from five years ago, but it's funny because a lot of people who interview me throw that line back in my face, so I guess I deserve it."

You get the impression that Furman is sure of who he is – and fame and glory don’t particularly factor in to his core happiness as both a human and as a songwriter.

“The audience is one thing and I’m not complaining, but what I really like is that there are some people in the world who I think use my records. Just a few; maybe one in a hundred, but they’re out there. I’m almost overly cautious about issues of ego, because I don’t want to believe that I’ve done a good enough job that I can be self-satisfied.

“Right now, I think I’ve made some fine records, but I can do better. It’s always about staying competitive with myself . . . Popularity is something that may happen from time to time, and I don’t trust it and I don’t think it means too much. I’m going for greatness.”

Ezra Furman plays The Academy, Dublin tonight. Perpetual Motion People is out now on Bella Union