He was adored by the Beatles, John Peel and John Lydon and signed by cult labels from Harvest and Virgin to Rough Trade and Creation, but mainstream success didn't matter a jot to Ivor Cutler. The ultimate outsider's outsider, he preferred to peer sombrely from the stage behind owlish glasses, singing his songs about bugs, herrings and his father pointing at thistles, his faithful harmonium wheezing along with him.

Next month, seven years after his death at the age of 83, the Glaswegian musician, poet and singer is being celebrated in a new touring play produced by Vanishing Point Theatre Company in association with the National Theatre of Scotland, whose previous productions include Gregory Burke's award-winning Black Watch and a stage adaptation of Swedish vampire film Let the Right One In. The Beautiful Cosmos of Ivor Cutler is named after one of his most tender songs (chorus: "This is our universe, cups of tea/We have a beautiful cosmos, you and me"). It takes the artist's work and life as inspiration, explains director Matthew Lenton, and experiments with them following Cutler's anarchic example. "I'd always thought of [our play] as being an anti-Mamma Mia," he says. "We wanted properly to illustrate what an eccentric Ivor was."

It helps that Cutler's biography is as rich as his songs. Born into a middle-class Jewish family in 1923, antisemitism and the Great Depression loomed large in his childhood, the latter influencing later works such as Gruts For Tea ("Daddy, we've had gruts for three years now. I'm fed up with gruts"), and his most famous sequence of songs, Life in a Scotch Sitting Room. Stories from his early adulthood also point towards his wayward personality. In the second world war, he was dismissed from the RAF for looking at clouds rather than navigating his plane, while his postwar teaching involved getting pupils to improvise a song about killing their siblings.

Cutler's musical career proper began on radio and TV in the late 1950s, however, and fame came when Paul McCartney caught him on the show Late Night Line-Up; a few years later, in 1967, he played bus conductor Buster Bloodvessel in the Beatles' Magical Mystery Tour. "I am your friendly courier," he says as the tour starts, darkly and dourly, as if announcing a journey to Hades. This demeanour had roots in real life too – a loyal member of the Noise Abatement Society, he even hated loud applause.

Cutler was embraced by indie circles in later years. He recorded a total of 21 sessions for John Peel's evening show between 1969 and 1991, and even had a minor hit in 1985 with Women of the World, which was released on Rough Trade (full lyric: "Women of the world take over/'Cos if you don't, the world will come to an end and it won't take long"). Creation Records boss Alan McGee even signed Cutler to the label when Oasis were in their pomp. His rebelliousness, playfulness and oddness won over all generations.

It continues to win the Vanishing Point team over, too, and Lenton keeps hearing new Cutler stories that make him laugh. One, from a Glasgow soundman he met recently, clearing up after a gig, is particularly evocative. "He heard a voice from the wings, going, 'Right, that's it. I told you, I warned you. I'm leaving you', and walked around the corner to see Ivor standing there talking to his harmonium." Abandoned there as promised, the instrument eventually ended up with the Celtic Connections festival team – but Lenton's team have it on loan now, and it will be centre‑stage for their tour.

"We love that the story behind it illustrates who he was too," Lenton adds. "Ivor was the sort of eccentric that's being squeezed out of the world now, the sort of person we should hang on to – he didn't live by the same rules as everybody else."

KT Tunstall at Glastonbury festival 2008 Photograph: David Levene for the Guardian

KT Tunstall

Singer-songwriter and Ivor Cutler obsessive

When I first heard Ivor Cutler about 15 years ago – on a mixtape King Creosote made me, I think – I was howling with laughter. My parents' idea of fun had been to get us camping in horizontal rain, so hearing Life in a Scotch Sitting Room and the parents dragging their kids out to look at nature – "Look, said father, a patch of grass!" – that really got me. Hearing him at the point I was entering into adulthood was also a massive relief. Here was an adult with a child alive and well inside. You're meant to suppress your inner child as you grow older, to gain approval, to be accepted, but he didn't. His was the biggest original rebellion. He didn't want to conform. He just enjoyed himself.

I've always found his music almost medicinal. If I'm on the road, emotionally bereft in yet another airport, I'll play Ivor and I'm calm. His harmonium's really magical too, as it sort of sounds like a person – I've played it on a few records because of that, and it's an incredibly human instrument. Ivor's songs remind me of the storytelling of Roald Dahl or Dr Seuss – they're all about simplicity, beauty and joyfulness, qualities usually belittled in rock music. Qualities people often see as weak, but which are anything but.

Robert Wyatt.

Robert Wyatt

Singer-songwriter, former member of Soft Machine and a friend of Cutler's. He recorded him on his 1974 Rock Bottom album track Little Red Robin Hit the Road

I first knew of Ivor after hearing Gruts For Tea on the radio. After that, [Soft Machine] would invite him to be our "supporting group" at gigs. We did not yet know about his Noise Abatement Society tendencies then or we wouldn't have dared ask. In person, Ivor was friendly, dry and funny. His music spoke to me as being neither quite comedy or tragedy – his work simply took you to another place, more like a sort of east European Samuel Beckett. In fact, he was dead chuffed when a radio producer said his silences were even longer than Samuel Beckett's.

His was a totally de-cluttered art, with self-imposed disciplines – he told us he preferred to finish a story by the end of the first page. Even in his longer stories, he avoided adjectival and adverbial clauses. He was all meat and no potatoes. As a singer he admired Paul Robeson, but the influence of the Jewish cantors in his own ancestry is also clearly detectable. I think Ivor's connection with musicians took his work out of the poetry ghetto, too – and I like to think he's still known by people who appreciate his uncategorisable range.

Norman Blake of Teenage Fanclub. Photograph: Tom Watkins/REX/REX

Norman Blake

Frontman of Scottish indie band Teenage Fanclub; covered Ivor Cutler with BMX Bandits's Douglas T Stewart and the National Jazz Trio of Scotland

I'm pretty sure that I first heard Ivor's music on the John Peel show when I was a young teenager, but I really started getting into him around 1981. Me and Douglas from BMX Bandits were in a school band together, making sort of absurdist pop music – some people say that we still are. Our main influences were Jonathan Richman's Rock 'n' Roll with the Modern Lovers and Ivor Cutler's Jammy Smears and Velvet Donkey. There was a wonderful simplicity to that music – Ivor and harmonium, Ivor and piano – that really spoke to us, and lyrically it made you feel like you could write anything you wanted. And it was fun.

I think that the people in Scotland who know his work will view him as a national treasure, although I'm not sure how many people are actually aware of him. He spent most of his life outside of Scotland anyway, and the themes in his work are universal. He is probably remembered mostly for his eccentricity and for his more outlandish and abstract work, but he wrote some really beautiful love songs. One of my favourites is Darling Will You Marry Me Twice? It's about a minute long, has five lines, and is heartfelt and incredibly moving.

I never met him but I saw him perform at the Assembly Rooms in Edinburgh in the early 80s. Just him and the harmonium – an amazing show. At one point he, rather curmudgeonly, asked the sound person to turn the PA off. "Too loud!" I loved that.

Kathryn Williams, singer-songwriter.

Kathryn Williams

Singer-songwriter;covered Beautiful Cosmos for her 2004 album, Relations

I was managed by Alan McGee for a few years, and he assumed that I would want to meet his big successes, Oasis. I was all, I don't give a shit about Oasis, you put out Ivor Cutler on Creation! And he went, "Ahh, there's a reason I did that, then… "

When I listen to Ivor Cutler, it makes me feel excited. It's a secret pleasure in a way, because you don't have people round for dinner parties and stick his stuff on. He also defines what it's like to be a proper eccentric. There's loads of people these days who think, "Oh, I'm a bit mad", and they're usually just loud people who talk a lot, and say things you know they're going to say. Ivor was the opposite of that. He made your brain turn around and flip over and think in a very gentle way, by creating these simple, beautiful, honest moments and sentiments.

I really love Ivor's quietness too. I take a lot of inspiration from him in trying to be brave enough to be myself, which is a quiet person, really. I played a gig recently where the crowd was pretty loud, and I thought, no, I'm going to do the quieter, odder, more heartbreaking songs anyway. Ivor had that really beautiful vulnerability in him which most people won't put across, but I've always followed his lead. He shows you how to be when there's nowhere to hide.

Jim O'Rourke, US musician and producer

Jim O'Rourke

US musician and record producer; covered Cutler's Women of the World on his 1998 album Eureka

Like a lot of people, I first encountered Ivor seeing Magical Mystery Tour. And as both of my parents are Irish, when I first heard Life in a Scotch Sitting Room, it wasn't that far from the sense of humour I had grown up around. His way with words, the darkness behind the seeming gentleness, made me think here was someone after my own heart.

I have as much [of his music] as I've been able to get my hands on, even his early album Who Tore Your Trousers? from 1961. I bought all the books of his I could in London, and they are still with me here in Tokyo – they're practically the only ones here. Probably, my favourite record is Privilege too. It's flawless. When I was in London, I used to go into his local bookshop in the hope of meeting him, but that was well before I covered Women of the World. I doubt that he would have liked it anyway. A little too loud probably.

Glaswegian singer-songwriter Alasdair Roberts treats us to a live performance of the title track to his album, Farewell Sorrow Photograph: guardian.co.uk

Alasdair Roberts

Folk musician inspired by Cutler; has covered his music at tribute gigs and on record

I first heard Ivor Cutler in the early 90s. There's a lot of humour in a his work, but I like his stuff that's not humorous at all. There's a poem on A Wet Handle called Flat Thin Chests, which is quite spooky and haunting; it influenced me a lot. His music puts across a real understanding of young people and children, from when he worked with them as teacher, and I respond to that too.

He was also really inspired by pibroch, this very traditional Highland bagpipe music. The folkiness of his music comes out of that, really. There's real subtleties and complexities to his work that I see as I get older as well, a real wisdom to his work. Such as, he was wise enough to realise that you can be silly, and that doesn't have to distract from intelligence.

I went to a few of his gigs in Edinburgh in the late 1990s, and got his autograph once. I remember he had very beautiful eyes. I just said thank you, as did he, and we both scuttled away, as it was meant to be.

George Martin, Beatles producer. Photograph: David Fisher/REX

George Martin

Record producer; recorded Cutler's 1967 album, Ludo, at Abbey Road

Ivor Cutler was one of a kind – quite the eccentric. Even in his normal speech he sounded as if he was lamenting the passing of a dear friend. I recorded him because he was such a character, and I had always enjoyed making comedy recordings and had some success. These were never significant, sadly [but] the Beatles were amused.