From dancing Blairs to Diana jokes, the Edinburgh Fringe musicals range from seriously funny to dangerously tasteless

The motto at this year's Edinburgh Fringe Festival is – make it sing, make it sing, make it sing. From Tony Blair's premiership to 1970s porn classics to the 7/7 massacres, every subject suitable (and many that aren't) has been set to music and shoved on to a makeshift stage, followed by a chorus of cha-cha girls. This is the year of the exclamation! mark! heavy! satirical musical. There is probably somebody reading the Edinburgh phone book to a reggae soundtrack in an abandoned church in Tolcross as you read this.

So what is the correct collective noun here: a flourish of musicals? A rash of musicals? Or a cancer of musicals? I set out to find the answer – and I began with a twin-set of Tony Blairs.

The endless Prime Ministerial speeches about The Legacy that filled the spring didn't include Blair's contribution to musical theatre, but it turns out the PM who dreamed of being a rock star has bequeathed two song-and-dance singalongs to this year's Fringe. At the Gilded Balloon, his story – in Tony Blair – The Musical – opens with a dark-robed, hungry peasant's chorus, lamenting the long winter of Tory rule. But then a red-tied Messiah emerges as the sun breaks over the Royal Festival Hall, and Blair's flattest clichés are leavened with music: "The art of politics is saying no not yes/ We have 14 days to save the NHS."

But this is, in fact, the Tony and Gordon story. Brown shambles on to the stage here as a chaotic, hyper-intellectual tramp, locked in a semi-gay sadomasochistic tango with Tony. His tie and his social skills askew, he gazes longingly at Blair's political skills and sings sweetly of their one-time partnership. But when Brown finally and bloodily dispatches Blair and takes centre-stage, Tony's corpse twitches back to life – and he is instantly reincarnated in a blue tie as David Cameron, to shunt Brown aside once again.

It's a neat conceit, but the news beyond the fringe – of Cameron's plummeting poll numbers, and Brown's bounce – shows the creators are too pessimistic. Yet there is real charm here. Sure, the music is too brooding and bleak for such a jaunty idea. Yes, the dialogue between the musical numbers collapses to the floor and slowly haemorrhages to death there. But this is a surprisingly intelligent way to process the Blair Years.

The rival Blair show-stoppers – in Tony! The Musical at C Venues – are weirder and worse. This is Blairism as an extended Footlights skit, where the PM proclaims himself to be "the love child of Martin Luther King and Madonna" and is haunted by the angelic ghost of Diana, Princess of Wales. ("Did it take you long to get here tonight?" he asks. "Only I've heard the traffic is murder.") There are moments of inspiration, like the four Tory leaders culled by Blair played as a bumbling barbershop quartet. But there are also moments of cheap, toxic bigotry: Peter Mandelson is presented as New Labour's Mr Humphries, a shrieking queen who plots to put cameras in men's toilets and is told by John Prescott (and this is a punch line): "You're a bloody poof!" Boom, boom. The show's likeable absurdist riffs hang, alas, on the brittle bones of a weak structure and weaker morals.

But this looks like Sondheim compared to the most obnoxious show on the fringe: Chav – Its'a a Musical, Innit?' at the Underbelly. The only way to describe this show is to explain that a bunch of rich kids have put on a show for more rich kids, to ridicule a particular branch of the poor, because they talk and dress differently to them.

Two sub-human "chav" girls waddle on to the stage, talking like this: "I ain't had a period in three months, Precious."

"You know what that means, Destiny?"

Her face crumples: "It means I'm dying, don't it?"

"No, you're pregnant."

"Oh yeah, OK, I'll go nick a pregnancy kit."

"Yeah nick me some lip gloss an' all."

The expensively dressed audience gurgles with glee.

Imagine an hour of it. With Little Britain and Catherine Tate, we do not see the effect of this undiluted class hate, because it is dispersed across a thousand television screens. But here, it is concentrated into one audience, and I spent most of the show watching them, their faces contorted with chuckling hatred for the voices, clothes and even the names of people who live on estates. Those people who say hatred of "chavs" is not hatred of the poor should hear the punch lines here: "I want to spend my life with you/ and our little baby too/ in our council home," sings one girl, and that's it; that's the joke – living in a council house. Oh, how the audience roars.

This "musical" exemplifies the contradictory abuse directed at "chavs". For much of the play, they are sneered at as BNP-supporting racists. But then – another hilarious punch line – they are jeered at for having actually having sex with black and Asian people and producing mixed-race kids, when one of the characters sings upon seeing "his" newborn baby: "There's nothing here of me/ It's a brown baby." What will the company stage next – Wog – The Musical?

Elsewhere, there is proof Bin Laden can be accompanied by piano and guitar too. One of these shows is a model of how to set terror to tunes; the other is a model of how to get it disastrously wrong. Failed States at the Pleasance Dome is advertised with a single stark image of the Tavistock Square bus, bloody and blown to pieces. Julie Andrews, stay home.

It is the story of a totally innocent Islamic air-conditioning salesman seized by an evil British police state and tortured for no reason. It sees jihadism as something that doesn't exist, except where the British state creates it by being mean to Muslims here at home. The sweet-faced jihadis presented here just want to talk, and dream of holidays in Sweden. Er... I think you've missed the point there. There are real and horrific dangers in over-reacting to jihadism – but this musical fails to dramatise them by being so facile about the initial threat.

Jihad – the Musical! at C Venues doesn't make this glib mistake. This is one "Jihad" that would reduce Osama to a ranting rage, puncturing his ideas with a needle-sharp and hyper-literate script by Zoe Samuel, who co-wrote the lyrics with composer Ben Scheuer. It tells the story of Sayeed, an Afghan peasant who is lured into training to be a suicide-bomber in a Western city. It doesn't show "respect" for fundamentalist ideas; it quite rightly pours acidic scorn on them.

There have been predictable hatchets in the press claiming that a show with numbers like "I Wanna Be Like Osama B" and "The Jihad Jive" are in bad taste. But one of the greatest tools against religious fundamentalists is irony. Their entire worldview militates against it; it punctures their literalist stupidity.

This is not a Bush-Cheney hymn, nor a protracted Republican attack-ad. On the contrary: Sayeed's jihadi handlers quickly fall into a symbiotic relationship with a Fox News ranter named Foxy Redstate, as they serenade each other: "I was foolish to doubt you/ For I can't live without you/ You're the best opposition for my cause./ You're the nemesis I dream of/ You're the reason my team of/ Angry millions wave their flags."

There have been polemics recently complaining about the lack of young musical writers, and I have endured endless musicals here that will feed that pessimism. But there are also glittering signs of hope – in the jihad, of all places. Somebody should sign up Samuel and Scheuer: there are whispers of Cole Porter in their jihad-mocking jingles.