Mysterious hooded figures in the town square. Inexplicable lights in the sky. Local traffic updates. Welcome To Night Vale might be one of the most popular podcasts in the world, but everything about it remains resolutely odd. It's an unsettling radio drama masquerading as a local community news programme. Imagine the overwhelming cosmic dread of HP Lovecraft, served up in a style not entirely dissimilar to BBC Look North.

Hypnotic and darkly funny, Welcome To Night Vale belongs to a particular strain of American gothic that encompasses The Twilight Zone, Stephen King and Twin Peaks, with a bit of Tremors thrown in. The setting is a sleepy-yet-creepy desert town where every conspiracy theory is real, but it's not really a big deal; the residents just try to get on with things amid the mayhem and horror.

"We didn't want to make a podcast that sounded like all the other podcasts we were listening to," explains Joseph Fink who, along with Jeffrey Cranor, has written every episode since Welcome To Night Vale launched in June 2012.

Fink, Cranor and narrator Cecil Baldwin met through the puckish theatre troupe the New York Neo-Futurists, and some of that anarchic spirit has seeped into Night Vale, a place where a love of the bizarre meets a love of language. "We agreed early on that we could write whatever we wanted, it could be weird and poetic, but it needed to have strict continuity," says Fink. "If we say something happened in Night Vale then it happened. Because the world needs to be believable within itself, even if it's not believable at all compared to our world." So Khoshekh, the hovering male cat that gives birth to kittens with poisonous spine ridges, becomes a beloved recurring character, and Night Vale's alarming mythology grows – throbs, even – with each fortnightly instalment.

Cecil Baldwin reprises his role as the narrator at a Night Vale live show. Photograph: Liezl Estipona

After a year, this eccentric outlier suddenly scuttled to the top of the US podcast chart, shutting out populist heavyweights such as Radiolab and National Public Radio behemoth This American Life (which averages around 800,000 downloads per episode). At Night Vale HQ, they'd registered a quantum leap in downloads in July 2013 but were struggling to explain it. "We couldn't work out where this spike had come from," says Cranor. "And the spike just kept happening. Then we started seeing links to fan art on Twitter and we realised it had grown on Tumblr through word of mouth."

This American Life may have since reclaimed the top spot, but Welcome To Night Vale remains a top five regular, though success hasn't altered the podcast substantively; it remains free to download, and free of advertisements, thanks to donations from fans.

"The process hasn't changed," says Baldwin, who still records Fink and Cranor's carefully crafted scripts by himself in his New York apartment. "I don't have a sound engineer or anything that would normally be associated with well-funded audiobooks. It's really just me trying to figure out how to take these amazing words Joseph and Jeffrey have written and bring them to life."

Baldwin, who shares a first name and a deep, mellifluous voice with Cecil – the sole narrator and de facto embodiment of Welcome To Night Vale – has guided listeners through nightmarish scenarios for more than 40 episodes. Has dealing with alien incursions, vengeful spirits and the machinations of the Night Vale PTA altered his worldview in real life? "Oh no, I was exceptionally strange before this podcast ever started," he says. "But what I'm discovering now is that people are ready for something that isn't so cut-and-dried, that doesn't have to be wrapped up with a nice moral message."

The global Night Vale fan community seems to have come to the spontaneous shared conclusion that Cecil has a third eye, likes to wear purple and has elaborate sleeve tattoos, judging by the reams of fan art on Tumblr. They've also seriously got behind the ongoing relationship between Cecil and visiting scientist Carlos, to the extent that fans cosplay as both characters at comic conventions.

"It's so refreshing and lovely, that a gay relationship has become a big part of the project but not the definition of the project," says Baldwin. The three Night Vale conspirators are currently in the middle of a sell-out live tour of major US cities, mutating the intimate podcast into something more theatrical, with guest readers and live musical guests. "Night Vale has totally changed our lives in a way that we didn't predict it ever would," says Cranor. "It's now a full-time job, in a good way." The downloads keep trending upwards, and a novel will be published next year.

Fink and Cranor are also getting used to fielding questions about the uncanny secret of Welcome To Night Vale's rocketship success.

"As a place, Night Vale is terrifying," says Fink. "There are a lot of things that don't make sense and people are dying constantly. But the thing about real life is that it's terrifying and there are lots of things that don't make sense and people are dying constantly. In Night Vale, it's aliens. In real life, it's cancer… but it's still the same thing. Cecil is giving you an example of dealing with the terrifyingness of life. I think that's partly what people are connecting to."

Welcome To Night Vale episodes are released on the 1st and 15th of each month. The live show is touring the US until 29 Mar. Visit commonplacebooks.com for more details