North Sea Scrolls, Cabaret Voltaire, Edinburgh<br/>Beardyman, Assembly Hall, Edinburgh<br/>Amanda F*cking Palmer, HMV Picture House, Edinburgh

Never mind the stand-ups, the best humour in Edinburgh came from an unlikely trio who delivered a secret history of the United Kingdom

An Englishman, an Irishman and an Australian walk into a Scottish bar.

It sounds like the set-up for a joke, perhaps the sort told by one of the comedians whose gurning faces adorn every upright surface in the city. But the humour in the North Sea Scrolls is altogether more mordant than that of the dead-eyed stand-ups whose only hidden agenda is to snag a TV contract.

The Englishman is Surrey-bred Luke Haines, leader of The Auteurs, Baader Meinhof, Black Box Recorder and author of the gloriously bitter Britpop memoir Bad Vibes. The Irishman is wild-eyed berserker Cathal Coughlan, formerly of Microdisney and The Fatima Mansions. The Australian is Wagga Wagga-born author, country singer and active seeker of trouble spots, Andrew Mueller. The trio, all wearing colonial helmets straight out of It Ain't Half Hot Mum, deliver a secret history of the United Kingdom in song and prose, via the vehicles of fictional actor Tony Allen and idiot diplomat-turned-dictator Martin Cahill.

It's a narrative that stretches from Moat (Raoul) to Mott (The Hoople), via the unlikely outposts of Hawkwind, The Angel of the North and the execution of Chris Evans, depicting a Britain in which Oswald Mosley became Prime Minister and heroin is free on the NHS.

A stern-faced Mueller introduces each Scroll with floridly purple passages, wielding a gavel with all the gravitas of a man who accepts being shot at in Israel and imprisoned in Cameroon as part of his job, whereupon the other two advance the storyline in songs which are by turns brutal ("Fuck the Pope and all you prods/Fuck off home and stop bothering God," croons arch-provocateur Coughlan), unexpectedly poetic ("Zeppelins fill the sky at dawn at Fishguard," Coughlan again) and bloody hilarious ("We have hanky, but no panky," sings Haines in "The Morris Man Cometh").

Never mind the careerist comedians. If the North Sea Scrolls don't make it on to BBC4 – actually, scratch that, CBeebies – then someone, somewhere is taking the pith.

The morning before watching Beardyman, I put a shout-out over Twitter. What things, I ask, are simultaneously impressive and pointless? The myriad answers include "ships in bottles", "tightrope walking", "people who can write prose on a single grain of rice", "the Moon landings", "the butterfly stroke", "serviettes folded as swans" and "all human activity". My intention was to gather ammunition for the assertion that human beatboxing – of which Beardy is a prominent practitioner – is about as impressive and pointless as it gets.

The ability to replicate a whole orchestra in your mouth, using only the plosives and fricatives of your lips, teeth and tongue, is of dubious value, especially on record (hence Beardyman's slightly underwhelming debut album). But 29-year-old Londoner Darren Foreman is an artist who absolutely demands to be seen live.

Don't be fooled by his appearance: a stoned slacker returning from a decade-long gap year. Beardyman's brain works at a higher processing speed than any of us. The first 15 minutes involve unaccompanied freestyling which goes way beyond music and into vocally-assisted mimes (if you'll pardon the contradiction) of, for example, a baby being put into a blender. The remainder of the show switches to hi-tech, using live looping from Beardy and Google Image searches from a Churchillian-looking sidekick called Mr Hopkinson. If the references are a little Noughties (Tony Blair masturbating a pig) or even Nineties (Stephen Hawking doing a single with Fatboy Slim), he wins full marks for delivering the heretical line, "Religion is merely consciousness-trauma", in a room whose main function is as the synod of the Church of Scotland.

The most stunning section involves a series of seemingly impossible improvisations – a reggae polka about Elvis and Top Gun, say – using suggestions from audience members. I'm one of them. "Are you doing a show?" he asks, lured in by my hairdo. "No," I say. "I'm reviewing yours."

Amanda Palmer, or Amanda F*cking Palmer as she's styled herself for this occasion, may not be as famed as Tori or Regina, but the former leader of The Dresden Dolls, the much-adored girl-Pierrot, boy-Chaplin duo from Boston who specialised in "Brechtian punk cabaret", has a following more rabid than any singer-pianist you care to mention. She's a magnet for the troubled outsider: every bisexual self-harmer in Lothian is here.

Wearing an outfit "crowdsourced" from Twitter, involving a silvery cummerbund and countless neckerchiefs which, along with the Adam Ant make-up, makes her look very sci-fi in a "final scene of Rocky Horror" kind of way, she and her Grand Theft Orchestra, which includes a belly dancer, a bagpiper and the extraordinary violinist Una Palliser stolen from Shakira's band, deliver a magnificent all-singing, all-dancing interactive revue.

As well as her own classics, there are four new songs, ranging from thumping electropop to a brassy, Dexys-ish stomp, a synchronised "fitness power hour" to Jacko and Men Without Hats, a ukulele cover of Radiohead's "Everything In Its Right Place", an inspired version of INXS's "Never Tear Us Apart", complete with sax solo, and two stabs at Le Tigre's "Deceptacon" (she forgets the words first time).

No two Amanda Palmer shows are the same. Tonight, guests include Edinburgh's own Horndog Brass Band and Georgia Train from Brighton's Bitter Ruin, who duets on "Delilah", but the star attraction is Amanda's husband, comic book author Neil Gaiman, who sings a song about Joan of Arc called "The Trouble With Saints" (killer line: "I wish you'd take a day off now and then ..."). It was written with Palmer, Ben Folds and OK Go's Damian Kulash as part of an "eight songs in eight hours" challenge, and sung with great reluctance by Gaiman. "We didn't make you sing," Amanda insists. "You had guns!" he protests. "We're American ..." she replies.

Next Week:

Simon returns to the mud for his zillionth Reading Festival

Rock Choice

The outdoor reunion shows were all very well, but hardcore fans are far more excited about seeing Pulp amid a partisan crowd at Brixton Academy, London (Wed, Thu). In festival-land, Jersey Live, at the Royal Jersey Showground, Trinity (Sat, Sun), hosts Plan B, Madness, The Ting Tings and – playing their last ever show – The Streets.