It is the fate of political leaders to be played by actors. In the circumstances Richard Nixon hasn’t been dealt a bad hand. He has been portrayed by Anthony Hopkins in Oliver Stone’s Nixon, by Frank Langella in Frost/Nixon on stage and screen and by tall handsome Christopher Shyer in Clint Eastwood’s J Edgar. But towering over them all is Harry Shearer, who has been impersonating Tricky Dicky since Nixon was actually president.

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".

A couple of weeks ago I was queueing to get into the BBC’s magnificently revamped HQ at Broadcasting House. Just behind me in the same queue were Harry Enfield and Paul Whitehouse. Their faces are craggier, their hair less confident than when the two comedians became part of the national furniture 20 years ago. And here they were, lightly joshing about the indignity of signing in to enter the offices of the national broadcaster which owes them so much.

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. Now La Stupenda is no more, Dame Edna is a gigastar and it’s her turn to shrill a gladdie-waving goodbye to her adoring public. She doesn’t look a day older, nary a hair out of place in that immaculate lilac coiffure.

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.

Autumn is a season of tumbling leaves, dark afternoons and of course fatuous memoirs from people off the telly. But every so often the world is taken by surprise, less by autumn itself than by the arrival of an autobiography by a genuine star that contrives to stand aside from the hideous commercialism of the bestseller lists. Such a book is Through It All I’ve Always Laughed. Or so its author would no doubt claim.

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.