Not long ago a group of naked cyclists attracted attention by pedalling through the streets of York in northern England to proclaim that “nude is not lewd” and “naked is normal”. Two years ago the artist Spencer Tunick swamped the front pages with nudity after persuading 1,700 Tynesiders to take off their clothes for an installation of communal nakedness in Newcastle and Gateshead in the north-east.

These very different events confirmed that mass cellulite and gooseflesh is, indeed, not very lewd. On the other hand, they were respectively a demonstration and a piece of performance art, both of which depended for their impact on the nudists’ second contention being precisely wrong. Clothed is normal because most of us prefer it that way and, by the same token, nude is news.

Now nakedness drifts even further north, as the Scottish National Portrait Gallery stages a nudathon of its own: two floors with more than 150 paintings, sculptures, photographs and drawings of people baring all over the past 150 years. The exhibition covers, or uncovers, a variety of “ordinary” subjects – the self, the lover, the parent, the child, the parent-and-child, friends, patrons, strangers – before finishing with a selection of celebrity flesh, most spectacularly Peter Howson’s full-length oil-portrait of the singer Madonna, her over-exercised muscles twisted like hawsers. It is a show bursting with interesting questions, explored further in curator Martin Hammer’s thoughtful catalogue.

In theory, naked portraiture is about the search for personality through nudity, which is what separates it from nude life studies, a comparatively objectifying and formal process. Barring a few royal mistresses, portraitists had steered clear of nakedness until the 20th century, at which point naked portraiture began to be something like a separable artistic genre all to itself. Freud had a lot to do with the theory. Artists became interested in stripping away the masks and costumes in which we “perform” ourselves, and looking for deeper truths, places where there is nowhere left to hide. John Berger underlined the point in the 1970s. The naked, he said in Ways of Seeing, was the real thing, while “the nude” was just wearing another kind of clothes.

So much for theory. In practice, matters are not so simple. A pioneer of this work was Egon Schiele, an artist fairly regarded as being as pitiless towards his sitters as towards himself. Here we see two views of his own naked body, a tortured stick insect with sinews and truncated limbs, a bare forked animal and nothing more. But Schiele’s chalk drawings of Erwin Dominik Osen are different. They portray his naked friend in the middle of a mimetic performance, apparently wearing make-up. Another cosmetic portrait in the show is part of a diptych by the photographer Robert Mapplethorpe. On the left he photographs himself in street clothes and on the right he wears nothing but drag make-up.

In fact, this exhibition is packed with men and women turning their nakedness into performance. Mapplethorpe gives us an exceptionally-endowed black man, his penis resting on a white stool like an exotic object on a plinth. Diane Arbus photographs a “Naked Man Being a Woman”, his genitals pinched out of sight between his thighs. Richard Avedon shoots Nureyev executing an extravagant dance-step. Philip-Lorca diCorcia snaps pole dancers. John Lennon, for Annie Leibovitz, pretends to be Yoko’s baby. Marc Quinn decorates his face with an ear, a nose and a tongue belonging to other people. Dustin Hoffman, by Sam Taylor-Wood, simulates weeping. And, inevitably, the Morecambe and Wise of art posers, Gilbert and George, show us their genitalia in stained-glass.

One of the most intriguing early 20th-century works here is “Self Portrait on her Sixth Wedding Anniversary” by the German painter Paula Modersohn-Becker. She paints herself, having recently left her husband in Germany to pursue art in Paris, stripped to the waist and cradling a bulging stomach in a gesture unmistakeably that of a mother-to-be. But the point is Modersohn-Becker was not pregnant and had openly and plausibly claimed not to want a child. Does the “false” pregnancy, coupled with the title of the work, hint at second thoughts about her life-changing decision? Or does it point teasingly, even tauntingly, down a path not taken?

Another lightly but decidedly feminist work is Cecile Walton’s “A Romance”, from the SNPG’s own collection. The painter was mostly active in the 1920s and in this, her masterpiece, she shows herself post-partum, lying naked on a bed holding up her newborn son while a uniformed nurse sponges her legs and her other son, aged four, looks on.

The catalogue entry sells the work short by suggesting blandly that the painting is about “searching for personal identity”. It dismisses the responses of Walton’s contemporaries, who pointed to parallels in Old Master art. But these parallels cannot be dismissed, since the painting is nothing if not a sophisticated riff on nativities, not so much those of Christ in his stable but of the more domestic birth of the Virgin Mary.

The Scottish National Portrait Gallery warns that unaccompanied children are not admitted to this exhibition, with the implication that they may find its erotic flesh disturbing. In fact, the most powerful works – in Berger’s sense of searching out what it means to be human – are about the fragility of flesh. Paintings by Lucian Freud and Francis Bacon show off their skills in this direction and an impassioned portrait of Patricia Preece does the same for Stanley Spencer. So, in very different ways, do oils by Alice Neel and the unflinching Joyce Gunn-Cairns, two painters astonishingly honest about age and disease.

The same can be said of Ken Currie’s life-size “Unfamilar Reflection”, a melancholy take on naked middle-age, based on the self-portrait element of Velázquez’s “Las Meninas”. Finally, of the paintings, I must mention a harrowing portrait by David Bomberg of his wife-to-be. In photography, the most striking works – by Melanie Manchot, Catriona Grant and Boris Mikhailov – are also about ageing. So parents need not worry. There is little of the priapic here, though much else to think and talk about.

‘The Naked Portrait’, Scottish National Portrait Gallery, Edinburgh, until September 2. Tel +44 (0)131-624 6200. Then at Compton Verney, Warwickshire, September 29-December 9