The voice on the phone sounds impossibly camp. It has a slick and persuasive way of putting things across, and I suspect it might belong to a salesman. ‘So, Mark and I met on a cruise,’ the voice tells me, a little over-confidently. ‘That was less than a year ago,’ it sing-songs, before adding with a breathless gush of excitement, ‘we just hit it off, and suddenly things are going absolutely great!’

Next, Mark chips in to give a little background on the tyre sales business he was running until last year. I’m too engrossed to interrupt, but the first voice does it for me. This time the camp twang has gone, and so has the salesman shtick. ‘Yeah, we thought maybe that sounded better than the truth,’ laughs Shenoah Allen, one half of Pajama Men, who actually met 15 years ago.

The comedy duo, who used to call themselves Sabotage, can’t resist a make-believe interlude, and during our chat they also pull a posh Londoner, a senile old lady and a depressed clown out of their imaginary props cupboard to meet me. Admittedly it’s less glamourous than the cruise ship fantasy, but Mark Chavez and Shenoah Allen actually met at high school in Albuquerque, while performing in a string of comedy improvisation groups. Their slow-burning career exploded when they brought a show to the Fringe in 2004. ‘Everything had fallen apart that year,’ remembers Allen. ‘Our original venue had collapsed, we’d lost our shirts and were performing to six people each show. We’d be staring at rows of empty chairs in the George Square Theatre and be like, “There goes another grand”.’

But in true showbiz style, just when they thought it was all over, they were snapped up by Second City, the legendary Chicago theatre group that kick-started the careers of Mike Myers, Bill Murray and John Belushi. Second City was where Saturday Night Live turned during the 70s when they needed new stars, and with their backing, Pajama Men got the clout they needed to launch themselves in the States.

Fast forward four years, and they’re sitting on three TV shows, all of which should be getting the green light any day now. Maple Maple Town is the working title for a comedy they’re developing with NBC; One Square Mile of Earth is an animation starring beer-drinking animals, and they’re currently finding a home for The Cody Rivers Show after filming the pilot earlier this year. ‘It’s the same game as it always was,’ says Allen, who was wearing his hair in three side-by-side Mohawks when he first approached Chavez in school. ‘It’s just a bigger playing field now.’

Both comics put the success of their double act down to the fact they never need to explain jokes to each other. ‘Our senses of humour meshed right from the start,’ says Chavez. ‘We quickly realised we shared the same sort of shorthand.’ It’s a shorthand they use most days now – consciously or not – when they take mental notes for new, preferably highly unusual characters. It happens anywhere: when shopping in Wal-Mart, caring for senile, elderly patients (something both Chavez and Allen have done in the past) or watching old-fashioned, tough guy movies like Ben-Hur. ‘Suddenly some new voice will show up,’ says Allen. ‘If it sticks around, and really works for us, that’s when we start developing a character. All these different personalities kinda end up writing the show for us.’

Some voices which have worked well for them can be heard in Versus Vs Versus, the typically surreal, physical comedy show they’re bringing to Edinburgh. Jennifer is a squeaky-voiced 14-year-old who ‘might possibly’ be possessed by the devil, and is on the run with dad, who ‘perhaps, maybe’ committed a small murder. There are also Roman soldiers, challenging each other in Mick Jagger accents, and some stiff upper-lipped 1950s newscasters tactlessly offending the subjects of their stories, and some ‘crazy seniors’ with speech impediments. ‘These are recurring characters that have stuck around,’ Chavez explains. ‘We retire them if we feel someone’s not pulling their weight.’

Pajama Men’s act relies heavily on physical theatre – they both use rubber-faced contortion and the energy of a few hundred bouncing balls to bring their eccentric skits to life – but Allen is worried that it gives some people the wrong idea. ‘Physical comedy always sounds vaguely immature and stupid, and words like mime and clown can be dangerous.’ He’s busy explaining that what they do is intelligent, with well-constructed jokes and clever word-play, along the lines of Demetri Martin or the cult US comedian, Mitch Hedberg (now dead), when Chavez interrupts, in the voice of a less-than-bright five-year-old: ‘Make us sound smart!’

Critics on both sides of the pond have been finding them both smart and very funny, and are generally in awe of the fact they need no more than two sets of nightwear to act out their weird collection of kids, evangelists, frogs or space ships. ‘We don’t have props or a set, just two chairs,’ says Allen. ‘It is challenging to make the characters distinctive without costume changes, but it’s also very freeing; you don’t have to worry about getting that crazy wig out the bag in time.’

Pajama Men’s routine is that welcome brand of original, slightly unhinged comedy, which also credits the audience with a certain amount of intelligence. ‘I really can’t stand those dull American sitcoms where it’s like a fat guy and a hot chick, and they somehow end up living together,’ says Chavez. They also hate anything boring, or obviously pandering to the masses. That and bad clowns. ‘Some idiot with a nose on, having a therapy session with the audience? They kinda stare at you for a while then ask you if you like them or not. You wanna say no,’ says Chavez, while Allen backs him up. ‘It’s like OK, we get it: your mother died. Now, bring the haha!’

Pajama Men, Assembly Rooms, 623 3030, 3–24 Aug (not 11), 7.40pm, £12–£13 (£11–£12). Previews 31 Jul–2 Aug, £5.