In Irish mythology, a stray sod is an enchanted piece of grass that, if stepped on, leaves a person feeling disorientated and lost, even in familiar surroundings. Although there's no reference to this in Tommy Tiernan's new show, Stray Sod, there's plenty of self-knowing stage Irishness – even, briefly, Oirishness – as he delivers a riveting 80 minutes of comedy that's a sort of state-of-the-nation address about his home country.

John Kearns introduces himself as himself as he comes on stage then, very carefully - tenderly almost - he lays out a blonde wig, a pair of women's high-heeled shoes and a skimpy dress on the floor. They stay there until the final segment of his show, untouched and without mention. He puts on a ridiculous oversize tonsure wig and a pair of joke-shop false teeth. Oh and he is wearing a horse costume, and “rides” Trigger as he performs the first bit of the show - which he tells us is about "disguise, expectations and failures".

Jane Bussmann may not be an immediately familiar name to some, but you will know her work. The writer, who was once a celebrity journalist, has been part of the writing teams for South Park, Smack the Pony and Brass Eye, among other quality television comedies, and wrote a hilarious memoir, The Worst Date Ever, about how a reckless whim took her to war-torn Uganda, where she helped unveil the appalling crimes of rebel leader Joseph Kony.

Six years away from live comedy (save for a couple of outings as MC for mixed-bill shows) haven't blunted Frank Skinner's stand-up skills. He's still an accomplished gag writer and performer, and his quick-witted comic's brain is, as ever, much in evidence in Man in a Suit at Soho Theatre in London.

Now here’s a funny thing, possums. Back in 1990 when one great Australian Dame, Joan Sutherland, gave her farewell performance, another, a certain housewife superstar from the Melbourne suburb of Moonee Ponds, seemed closer to  retirement age.

We shouldn't expect a perfectly formed show with a narrative arc and a final gag that is a series of clever callbacks and which neatly encapsulates all that has gone before, Stewart Lee tells us at the beginning of this show. Much A-Stew About Nothing is a sort of work in progress, as the comic tries out material for the BBC television series that he starts recording at Christmas and which will be on our screens in the spring. As such it's a more loosely formed enterprise than previous live shows and includes a lot of material that may not make the final cut.

Massachusetts-born Bo Burnham first performed in the UK at the 2010 Edinburgh Fringe. The then teenage prodigy, who had come to fame as a YouTube sensation, took the festival by storm and was given the Edinburgh Comedy Awards' panel prize. He hasn't performed here again until this year's Fringe, when his second stage show, What, sold out in a matter of minutes and was again garlanded with rave reviews.

Sarah Millican’s career blossomed on the back of a divorce. Her husband upped sticks after seven years of marriage when she was 29. The rage and sorrow catapulted an innately funny office worker into a second career. For her new show, entitled Home Bird, the story has moved on and her subject is buying a home and installing her boyfriend. Only he’s not happy with the arrangements in the garden. The shed, he complains, is not suitable for self-abuse. That, Millican explains, is because it’s a greenhouse.

Most years at the Fringe, there's considerable division over the winner of the Edinburgh Comedy Award, but not in 2013 when Bridget Christie won for A Bic For Her, a show that expertly fillets everyday sexism and misogyny. Even those who remarked that they never knew feminism could be funny - idiots all, of course - acknowledged the show is an hour of superbly crafted comedy.

When Andrew Maxwell premiered Banana Kingdom at the Edinburgh Fringe earlier this year, its title made a lot more sense. The show was a coruscating examination of what Scotland might be if the independence vote next September goes Alex Salmond's way; a tiny nation trying to go it alone at a time when the rest of Europe wants to be an even bigger - and of course happier - family.