Edinburgh attracts splendid eccentrics who leave anonymous poems in buses, or perform 10-minute dramas for an audience of one in the back of a car, or abseil down Salisbury Crags reciting Morte d’Arthur. There is also a crowd of naive vanity actors (and others) who lose money in empty halls. But the stalwarts of the Fringe are teachers who see the festival as an unmissable performance opportunity for their students.

In the front rank of these is Leicestershire Youth Arts, who this year celebrate their 25th visit to Edinburgh. The tradition began as a school visit, but then the two teachers who organised the trip were offered early retirement. They carried on, self-employed, creating a county arts service for young people and every year the pair bring a half-dozen productions to Edinburgh, with 70 students to perform, stage manage and run the venue. For this, each one gets a vocational qualification equal to an A-level.

With every succeeding year, director Robert Staunton laments, it is “harder to find different plays and musicals which will challenge the students and sell tickets”. This year the search led him to Stephen Sondheim’s Company, the ground-breaking musical the composer hoped “would have the audience screaming with laughter and then go home and not be able to sleep”.

This ruthless entertainment shows four couples trying to persuade their bachelor friend to try matrimony, despite the powerful counter arguments of their own failed marriages. George Furth, who wrote the original stories, thought it could all happen inside Robert’s (the bachelor’s) head. Staunton seizes on this idea quite brilliantly, caging the unmarried man in a small, hazy triangle of piano, bar and sofa, the married couples emerging from nowhere for their tireless assaults on his singleness, pounding the nagging songs into his head as well as ours, until he reaches breaking point, though what that actually is Sondheim leaves unsaid. It is immensely watchable and the cast deserve their A-levels every night.

A much larger stage was needed for the 70 actors, orchestra and technical crew of the drama department of E. C. Glass High of Lynchburg, Virginia, and their production of A Chorus Line. This was the school’s fifth time at the Fringe, as part of the welcome annual invasion by the American High School Theatre Festival.

Like Leicestershire Youth Arts, the school uses the Fringe as part of their dramatic arts training and is proud of the students who go on to win acclaim on Broadway, at regional theatres, on television and in films.

There will be more, to judge by this show, which was on for just four nights.

This fascinating musical takes the form of a prolonged audition, where, after going through the dance routine, the tyrannical producer obliges the wannabes to step forward from the line and expose their private lives in front of their fellows, and the audience of course. The endlessly smiling faces and robotic high-kicking heels give way to the painful, long and winding roads these hopefuls have travelled to fight for their place under the bright lights. The monologues are based on real-life accounts by New York performers and are salutary biographies for the students as well as tests for their drama skills.

Seeing these students was like watching fish in water. Justin Bowen danced and sung his way through “I Can Do That” with charming fleet-footed aplomb.

Jessica Sumpter managed to convey a world-weary resignation in singing “What I Did For Love” and Eric Pearcee was the almost statutory larger-than-life character in these American shows, with a personality to fill even a decorous temple like the Church Hill. The finale, when in the quickest of changes the company abandoned their rehearsal clothes for the gilt and glitter of show-time, looked like the real thing.

Far from the real thing are the inverted pirates in the children’s show The Ignatius Trail, deep in the vaults of the Smirnoff Underbelly. The lookout is blind and much given to groundlessly bawling “Land ahoy!”, another pirate is a romantic poet, the captain doesn’t know what any parts of the ship are called, and his slave mostly sunbathes on deck. They support their futile wanderings and their robust a cappella singing by extravagant social security claims until their idyll is interrupted by the visit of a virago from the pirate inspectorate.

The engaging Dan McGowan (excelling in his fight with the invisible monster) is the strangely named Ignatius Trail. How he survives walking the plank and the attentions of the ugliest mermaid in the world to bring peace and indolence back to the ship is a tale of agreeable nonsense, by turns cheeky, fiercely dramatic, goofy, suave and operatic.

The En Masse theatre company, deftly led by Amy Leach, is a bundle of acting and musical talent. Oliver Birch’s off-the-wall story makes its own rules and seemingly needs no other message or moral than that you should keep your promises and always carry a copy of Shakespeare’s Tempest. This and casting the writer as the slave are but two of the private jokes the cast enjoy.

If you want a message, try Wells Fargo, as the Hollywood mogul snarled. Or you could have gone to see I Theatre’s Dancing with Dragons, another children’s show, this time an anthology of traditional stories from far east, from New Zealand to China and India. Brian Seward directed, coming back to Britain, where he once had helped to make nuclear submarines and had been head of a school drama department.

The show was premi red at home in Singapore in the Asian Children’s Drama Fiesta last November and has the responsibility of representing Singapore and the Asian-Pacific region on the Fringe. It was a burden it carried lightly and with grace.

After a leisurely start, by Western standards, the four performers charmingly danced, acted and mimed their way through nine improving tales, from how the jackal saved the brahmin from the tiger (south India) and how the prawn caused trouble (Burma), to the spectacular tale of the four dragons (China).

The theatre style was a blend of Asian and European and the same cross-cultural work came with the cautionary stories, tales of cunning and myths of explanation which echo European folk stories in their form and intention. More exotic was the accompaniment created by Joyce Teo and played by three on-stage musicians on a variety of gamelan instruments.

In contrast, the Bristol Old Vic brings to the Assembly Rooms its adaptation of Private Peaceful from the novel by Michael Morpurgo. The prolific and successful children’s laureate is an articulate champion of children’s arts and children’s theatre in particular. For this story, he turned to the carnage and privations of the First World War and the almost 300 British and Commonwealth soldiers who were executed for desertion and cowardice, two of them for sleeping at their posts.

In Simon Reade’s skilful adaptation we meet Tommo Peaceful in his army cell on the night before he is to be shot at dawn, determined to spend all the minutes he has left in remembering his short life. He begins with his first day at school and takes us through his schooldays, the death of his father, his devotion to Molly who marries his staunchly loyal elder brother Charlie, and his first working days as a 12-year-old casual farm labourer.

The beauty is in the detail and the internal echoes as we see his narrow world through his eyes, and his acceptance of poverty and the repressive social system, personalised by the bullying figures of the schoolmaster, the squire and the sergeant-major.

Because we see the war from his viewpoint and limited understanding, the story can give even the youngest theatre-goers an insight into a slaughter which still baffles adult understanding in the immensity of its horror.

There are grim echoes of the popular song “Two Little Boys” when Tommo refuses to leave his dying brother in a shell-hole in no man’s land to go forward on the vindictive Sergeant Hanley’s suicidal attack and, in consequence, goes before the firing squad.

In this one-man show, Paul Chequer gets into the skin of Tommo, even to the innocence of a country boy who had never been taught to think for himself.

The actor took two warm curtain calls and could have had more.

Company, until August 21, tel 0131 557 0469 The Ignatius Trail, until August 29 (not August 24), tel 0870 745 3083 Private Peaceful, until August 29 (not August 23), tel 0131 226 2428 www.edfringe.com