The trend of celebrating anniversaries by digging out old classics might suggest that no good new plays are being written, but at least it gives us the chance to re-assess their worth. Theatre Royal Stratford East, the legendary Joan Littlewood’s old venue, presents a new production of Oh What a Lovely War in its 60th anniversary year to coincide with the 100th anniversary of the First World War. This classic, first staged in 1963, is a powerful anti-war tract — but is there any more to it than a flamboyantly theatrical humanity?

Would you be able to tell if the world had ended? For Beth and Franklin, the wannabe intellectuals at the heart of Stephen Sewell's play, it proves quite difficult to ascertain whether life as they know it has come to an end from their privileged life high in a luxury Melbourne apartment. Whether they are bickering about how the New Yorker has gone downhill or despairing about terrorism, they remain insulated from the world by their own self-absorption.

An insider once told me that you get a grant for including puppets in a production. Which may account for the amount of crap puppetry haphazardly applied in the theatre. That certainly can't be said about the work of husband-and-husband team Adrian Kohler and Basil Jones of Handspring as they collaborate again with War Horse director Tom Morris, this time on Shakespearean texturing of organic discipline. The problem is that such focused visual imagination needs to be matched by verbal beauty, word magic, of the highest order, and it isn’t.

Plunging into the lonely vortex of the long distance web wanker isn’t obviously gripping theatre, but Chris Goode’s seventy-minute descent into tawdry solitude and digital fantasy doesn’t do too badly.

What exactly is unconventional about an unconventional couple? In Abi Morgan’s new two-hander, an adaptation of last year’s book of the same name by She and He (a West Coast American couple now aged 90ish), the situation is simple. Boy meets girl at college, they lose touch, then meet again 20 years later, when both are married with kids. When they start an affair things go wobbly, but then she asks him to sign an agreement: in return for a house and income, she will provide him with “mistress services”.

The best thing about this show is its title

Canadian playwright Matthew Edison's award-winning 2003 play The Domino Heart receives its European premiere in rather reduced circumstances. As a Sunday to Tuesday production at the Finborough (directed by Jane Jeffery), it takes place on the set of another play (Chris Thompson's Carthage). Luckily the play itself is essentially a shared act of storytelling. Three characters deliver monologues to the audience while the others read, write, doodle and generally act as if they're not hearing one another.

In 2011 Tim Pigott-Smith gave us an impressive, humane King Lear at the West Yorkshire Playhouse. Here he is again, a patriarch learning how "sharper than a serpent's tooth" it is to have thankless children, but this time his character decides to do something about it and to acknowledge his own failings. The result is good-natured comedy rather than tragedy.

There’s no place like home – and home for writer Simon Stephens is Stockport. He doesn’t live there any more, but he was born there in 1971 and still finds the place, particularly its seedier side, a rich source of emotionally charged material. So, having started life less than 10 miles from the Royal Exchange, he keeps coming back. This is the fourth play he has written for the theatre, starting with Port in 2002.

Barely a month of 2014 has passed, and yet already the opportunities to remember the First World War seem to be presenting themselves at every turn. In this trio of short plays, we get a more unusual treatment of the anniversary – as the overall title suggests, the purpose is to hear the voices that don't sound so loudly across the intervening hundred years. We are here to understand what the women did in the war.

Sam Mendes thinks King Lear is a bigger play than it is. In a new staging he directs at the National Theatre, he wants it to be about a convulsion of nations, a reordering of borders, bombing populations. When Lear arrives to carve his kingdom into three - entirely in his own self-interest, not his daughters’ (in the play) - over 30 soldiers are stood to attention rear stage. The illusion suggests 300 and proposes that this is a ruler whose every command is enforced by the mere shouldering of hundreds of guns.