In 1170, as you no doubt know, America was discovered by the renegade Prince Madoc of Wales. Six hundred years later, history repeated as both tragedy and farce, when a young adventurer from Caernarfon, John Evans, crossed the Atlantic in search of Madoc's descendants, a lost tribe of Welsh-speaking Native Americans. Now, 200 years on, it repeats as dotty prog-pop cabaret, as Super Furry Animals frontman Gruff Rhys relates – in concept album and ramshackle stage show – his own voyage up the Missouri in trace of Evans, whom he claims as a distant relative.

Like his ancestor, Rhys has leapt into the unknown – or at least, it seems that way, as his iPad flashes "low battery" warnings and he blithely disregards the conventions of narrative music-theatre. Half-hidden under a Davy Crockett hat fashioned from toy wolf, Rhys plays faux-naive Welsh bumpkin and implies Evans was the same: an innocent abroad, engaged on a half-epic, half-ridiculous quest. He lets the comedy of the Madoc/Evans story emerge in nuggets of gentle deadpan. "The one problem," he sing-songs when Evans finally reaches the sought-after Mandan tribe of north Dakota, "was that they didn't seem to be very Welsh."

It's an irresistible tale, rendered in rickety fashion by Rhys. The history is regurgitated as 1970s documentary (screened as an introductory primer), slideshow drolly starring a muppet version of Evans, and songs scored by acoustic guitar, metronome and effects gadgetry. It's haplessly fragmented, and the songs do nothing so orthodox as explicate or dramatise Evans's journey; they're more tangential than that. But tracks such as Lost Tribes and Walk Into the Wilderness form the swelling heart of the show and, courtesy of Rhys's pellucid voice, they release the romance of Evans's adventure and the rich mysteries of the new world when it was new and unknown.

• Until 10 May, then touring. Box office 020-7478 0100. Venue: Soho theatre, London.