Josie Long, Pleasance Courtyard, Edinburgh Trevor Noah, Pleasance Courtyard, Edinburgh Alan Davies, Venue 150 @ EICC, Edinburgh Jessie Cave, Underbelly, Edinburgh Back to School, Pleasance at Braidwood Centre, Edinburgh

To use a bit of Cowellian parlance, Josie Long has been on quite a journey in recent years. I mean, who knew that an act once marginally twee-er than a Bagpuss tea cosy would be the one to rescue political stand-up from its New Labour-era doldrums? However, her latest show, Romance and Adventure, begins with a less metaphorical, more muscle-exerting trip: a mountain climb in Kenya that left her troubled by her penchant for "super aristocratic" pursuits. It's the cue for a vexed life appraisal, fuelled by turning 30, in which feelings of political and personal inadequacy elide. Why, she wonders, does she continue to shop at her corporate bête noire, Tesco? And, as a bona fide leftie, is she destined to "be born, live, fight and die" on the losing team in any case?

Well, no, is the Long and short of it, as her familiar optimism returns via renegade touring, Alasdair Gray quotes, and naming her toilet "Michael Gove". Indeed, though the show may be predicated on insecurity, her smiley subversive shtick is more self-assured than ever. She's always been a wonderfully conversational performer, but here there are great set-pieces, too: you'd have to scour Edinburgh far and wide to find a single skit funnier than her transformation of Ed Miliband into a roughneck revolutionary. And where she's previously apologised for her principled fury, now she gives it gloriously free rein. "If you haven't done anything for charity by the time you're 29," she snaps, "then what you could do is jump off a building – and, by all means, get sponsorship." A slightly pat – and, yes, twee – sign-off leaves a few too many questions hanging. But the main one is: how long can the Foster's Comedy Award continue to escape her now?

As for the newcomers category, buzz would suggest that the South African Trevor Noah is a strong bet. The mixed-race comic's identity angst is the cornerstone of this Edinburgh debut: a substantial topic, given that he was "born as a crime" to an illegally partnered white Swiss father and black Xhosa mother during the apartheid era. The salve, though, is that it has afforded the boyish 28-year-old a privileged perspective on the absurdities of racial demarcations and assumptions in his home country and beyond. His show, The Racist, spins off from an eye-opening trip to the US, where, hoping to be embraced as black, he instead encounters whole new strains of prejudice – for example, the way mixed-race celebrities are recategorised as soon as they become successful. Similar observational jewels stud an hour that benefits from the quiet authority of Noah's deceptively soft-spoken delivery – and whether mimicking Obama or a casually bigoted Kentucky fan, he makes for a deft impressionist to boot.

The doomy title of Alan Davies's new show is Life is Pain, although "Life is a Pain" would better sum up its desultory disgruntlement. Back on stage for the first time in a decade, the fortysomething star uses his return to bore on about the developments of the intervening years. So we get wide-eyed bafflement at social networking, smartphones and internet porn, and misty-eyed nostalgia for student japes, dial phones and the lingerie section of the Freemans catalogue.

At one point, he even, bafflingly, makes a meal out of Facebook poking, an activity and comedic subject that one's maiden aunt would likely consider passé. Suffice to say, it's a plodding, superficial hour, with occasional lurches into crudeness that smack of showboating desperation. There's one good passage, in which Davies imagines the thoughts of his crying baby; it's just a shame that his own psyche remains elusive by comparison.

Allow me to regress a little. Representing Hollywood this year, albeit tangentially, is Jessie Cave, a 25-year-old actress who starred in the Harry Potter franchise. Riffing off her association with childhood fantasy, Bookworm sees Cave hosting the inaugural session of her new book club amid a Play School-style set complete with cardboard Wendy house. However, as she obsesses over The Lion, the Witch and the Wardrobe and freaks out over Fifty Shades of Grey, it becomes clear that literature is providing unhealthy amounts of escapism for this mildly deranged woman-child. It's a curious, compelling fiction, with something of the warped whimsy of a Wes Anderson movie, and its scattily charismatic star is certainly one to watch – as is her teenage sister Bebe, playing the most delightfully gormless comic sidekick since Dame Edna's Madge.

Sillier still is Back to School, an immersive production that transforms a community centre, an outpost of the Pleasance, into the shambolic secondary St Dumbiedykes and provides us, its pupils, with a whistle-stop bad education. The press blurb's claim that the piece is a response to the "psychological experiments of Milgram and Zimbardo" seems a fanciful way to dress up an hour and a half of jolly nostalgia kicks. But, in that respect, it works admirably, with the committedly eccentric performances of the teaching staff provoking committed mischievousness from the student body in return. Though, split into different "forms" as we were, I was sad to have missed out on the sex education class.

Please, sir, can I have some more?

Jessie Cave and "Back to School" to 26 Aug, Josie Long and Trevor Noah to 27 Aug ( all 0131-226 000); Alan Davies begins a UK tour at Venue Cymru, Llandudno, on 5 Sep (0844 844 0444)