The art of the Chicago Imagists of the 1960s and 70s provokes spluttering questions, and answers in a similar spirit. Incarnated as the Hairy Who, the Nonplussed Some, and various other names reminiscent of niche 60s rock groups before they made it big, the artists who came to be known as the Chicago Imagists (not a bad band name itself, come to think of it, if a bit too arty) were cartoonish and clever and possessed of a wayward graphic elan. Now at Goldsmiths Centre for Contemporary Art in a Hayward travelling exhibition, this is the first UK show of their work in almost 40 years.

All alumni of, or teachers at, the School of the Art Institute of Chicago in the fervent era of student protest, political assassinations and the Vietnam war, the Chicago Imagists were very much of their time and place. But little of the cataclysmic events surrounding the 1968 Democratic Convention in Chicago – with mayor Richard J Daley’s police running amok, and the air filled with teargas and Mace – got into their art, except by way of the curdled, visceral quality of many of their images.

Facebook Twitter Pinterest Officer E Doodit, 1968, by Jim Nutt. Photograph: courtesy David Nolan Gallery, New York

Jim Nutt, one of the founders of the Hairy Who, came closest to referencing Chicago politics with his 1968 profile portrait of Officer E Doodit, a smiling, thick-necked goon with snot ballooning from his nose, foaming teeth and some kind of goo leaking from his ear. Not to mention his shaving scabs and pustular zits. Nutt’s Snooper Trooper, from the previous year, is equally horrible, a peanut-brained walking paroxysm spluttering something horrible into a tiny specimen glass.

Nutt mostly painted on the underside of sheets of plexiglas, giving his work a flat, enamel-like shiny sheen. Chicago is the home of the pinball machine – many made in Chicago’s north side by the Gottlieb family. The twitching flippers, the squawks, bleeps and boings of the sound-effects, the rattle of the ball and the electrified, lurid, lit-up graphic madness of the pinball table got into Nutt’s art, as well as that of other artists. Nutt’s wife, Gladys Nilsson, Art Green and Karl Wirsum all appeared to partake of this same juddering freneticism. The pinball machine is a raft of images and action brought to life by the twitching, buffeting human body, and bodies and bits of bodies in motion are everywhere in the work of the Imagists.

Nilsson’s funny, grotesque, nightmarish figures, whose origins lay in 1930s cartoons and animations, are filled with bodily extrusions, infestations of bird-like beings and often manic action. I wouldn’t want to look at her 1968 A Cold Mouth if I were contemplating an acid trip. Although these artists were hard at it in the late 60s, and there were parallels between the Imagists and underground comics, drugs don’t seem to have played much part in their circle.

It wasn’t all mad, bad drawing, although Karl Wirsum’s screechy post-psychedelia revelled in eye-popping nastiness. Two of Wirsum’s cut-out painted wooden figures, which nod to one another as they dangle from the ceiling, are suspended from screwdrivers driven into their backs. They hang there, oblivious.

Facebook Twitter Pinterest Ice Pick Nick Fisherman, 1979 by Karl Wirsum. Photograph: courtesy Elmhurst College Art Collection

Is that a ring of dangling testicles in Sarah Canright’s untitled, mandala-like, pastel-pale 1968 painting? What a strange sort of hypnotic, transcendent image this is. Female bodies, wrapped and bound and muffled in strange corsetry fill Christina Ramberg’s images. They have a fetishistic feel. Ed Paschke, often called Mr Chicago, made lurid, embellished, seedily fluorescent images of tattooed carnivalesque party girls and performers, painted pin-ups in sickly light. Ray Yoshida’s pictograms, sometimes bouncy, sometimes sinister, seem to look forward to Keith Haring and backwards to surrealism.

Personally, I like Roger Brown best. His atmospheric, nocturnal street scene, The Girl, from 1969, with its silhouetted protagonist wandering between obelisks and wrapped monuments, set among freeway flyovers and the passing lights of distant trucks, carries marvellous unhinged echoes of Giorgio de Chirico’s metaphysical paintings, transposed from interwar Turin to a dreamlike Chicago. Another four-panel street scene repeats the same night-time image four times, with his fellow artists visible in lit windows, and strangers caught in private acts in their apartments. Somehow, Brown is channelling both the voyeuristic Jimmy Stewart in Alfred Hitchcock’s Rear Window and Edward Hopper’s Nighthawks (which is in the collection of the Art Institute of Chicago) in this delicious play of shadows, neighbourhood streets and yellow, artificial light. I can imagine The Simpsons creator Matt Groening loving this. I do too.

Facebook Twitter Pinterest Roger Brown, The Four Seasons – A Benefit Painting of the Hyde Park Art Center, 1974. Photograph: The School of the Art Institute of Chicago and the Brown Family. Private collection, courtesy McCormick Gallery, Chicago

Chicago Imagism wasn’t simply a belated pop art, but it did revel in popular culture, image-scavenging, sharing gags, riffing and having conversations with one another. The Imagists went their own way, largely oblivious to minimalism and post-minimalism, conceptual art and the last-gasp death throes of post-painterly abstraction. It was, and is, a Chicago thing.

• At Goldsmiths Centre for Contemporary Art, London, until 26 May, then De La Warr Pavilion 15 June – 8 September.