Like a bodybuilder on a diet of protein shakes, the annual appearance of the Edinburgh Art Festival (EAF) on the capital's cultural stage finds it looking ever bigger, bulkier and, as they say in gym-land, "ripped".

Underlining the idea that this is now a festival which is well-muscled and capable of heavy lifting, some of the most notable shows in the 2015 programme - John Chamberlain at Inverleith House, Phyllida Barlow at The Fruitmarket Gallery and Kennardphillipps at The Stills Gallery to name just three - feature monumental sculpture and towering installations.

A side theme this year is performative video work by young female artists, most obviously Anglo-Finn Hanna Tuulikki and Edinburgh-based Irishwoman Emma Finn, and at the chewier, intellectual end of the spectrum the programme offers a fascinating dip into the oeuvre of reclusive German conceptual artist Hanne Darboven, whose ever-changing but relentlessly repetitive pages of numbers line the walls of the Talbot Rice Gallery. There are 754 framed pages in all, from a total of 2782 completed by the time of her death in 2009 aged 68.

There's stardust aplenty too: literally, in the form of the blockbuster David Bailey retrospective of that name at the Scottish National Gallery, but also in crowd-pleasing exhibitions looking at the work of MC Escher (at Modern Two), Roy Lichtenstein (Modern One) and the relationship between Pablo Picasso and American photographer Lee Miller (Scottish National Portrait Gallery).

Perhaps the best place to start is where many visitors to Edinburgh do - in Waverley station, home for the duration of the EAF to Charles Avery's Tree No.5 (From The Jadindagadendar), a metal sculpture which looks like a series of Parisian lamp-posts welded together and adorned with long tubes of coloured plastic. They could be sweets, they could represent ribbons or rainbows, they could be something else entirely. "Feel free to touch," is the message from the omni-present EAF volunteers. They swing, but won't chime.

Turn round and leave the station via the bridge to Calton Road, enter the rarefied Ingleby Gallery and climb the stairs, and you'll find a 2D representation in pencil and ink of someone else doing what you've just done. Called Untitled (Girl Standing In Front Of Tree Five), it's part of Avery's engaging new show, The People And Things Of Onomatopoeia.

For the Oban-born artist, Onomatopoeia is a fictional place and the new works form another chapter in his ongoing Islanders series, the lifelong project in which he will map Onomatopoeia's people, its belief systems, its architecture, its furniture, even its nightlife and road layout. The large-scale drawings alone are terrific, but throw in the background and the many moments of fun - I particularly like the poster showing a rhino and bearing the legend "Looks like a unicorn, smells like a unicorn" - and you have one of EAF's most pleasing shows.

I'd put Here Comes Everybody at the Stills Gallery into the same category. Nobody could ever describe the work of Londoner Peter Kennard and Edinburgh-born Cat Phillipps as subtle, but then what's the point of sneaking up on viewers from the side when you can shout in their faces? And shout they certainly do. Their best-known image is the one of Tony Blair taking a selfie as the Iraq oilfields burn behind him and they're no less withering in their treatment of the political classes and their accompanying elites in this new show.

Last year they exhibited in a room at Summerhall and the ramshackle venue suited their chosen media, predominantly old bits of wood, video monitors, piles of newspapers and massive "canvases" cobbled together Heath Robinson-style from the Companies & Markets pages of the Financial Times.

In the relatively august surrounds of the Stills Gallery this same approach is even more thrilling and powerful. The artists have created sculptures out of pallets, lined one wall with images framed using the same kind of wood and brought more of their FT-baiting image-making and sloganeering to the rest of the space. Onto these newspaper pages they superimpose images of rough sleepers and food banks.

The best piece is a relief of sorts and shows a young man - what the politicians used to call "a hoodie" - pushing at a piece of paper which crumples outwards. On it is printed a picture of David Cameron in black tie quoffing something from a wine glass against the skyline of the City of London. And just to prove that the artists are democratic in their disdain - or maybe just that they watch Game Of Thrones - one of the video pieces is titled A Song Of Oil, Ice And Fire. If you like Banksy, you'll love this.

There's more sculptural humour at work in John Chamberlain's show at the light-filled Inverleith House, too little recognised but one of the gems in Edinburgh's visual arts tiara. Downstairs are examples of the work for which the American is best known, colourful sculptures made from bits of cars, while upstairs are smaller works, like the beautiful series of "sockets" he made in 1978 by casting old coffee tins in aluminium then painting them in iridescent colours. Also upstairs are a series of foam strips twisted into odd shapes are all titled Stuffed Dog while in the basement you can watch The Secret Life Of Hernando Cortez, the trippy 1969 film Chamberlain made with Warhol acolytes and Factory "superstars" Ultra Violet and Taylor Mead.

Outside in the grounds of the Royal Botanic Gardens are four late works in pink, blue and green, massive scaled-up versions of the circular tinfoil maquettes Chamberlain was making towards the end of his life. The artist died in 2011 and, incredibly, this is his first UK show, so kudos to Inverleith Gallery for that too.

At the heart of the EAF programme is its commissions. Charles Avery's station installation is one of them and along with the other six they're grouped under the banner of The Improbable City, an idea inspired by Italo Calvino's 1972 novel Invisible Cities. It imagines a dialogue between explorer Marco Polo and Yuan dynasty founder Kublai Khan, of Xanadu and "stately pleasure-dome" fame.

For the purposes of the EAF, the idea translates into those imagined spaces and regions where the probable and the improbable meet. Some of the seven artists have abstracted the notion to the point where it's barely discernible, but clearly it courses through Avery's work and it's equally evident in the work of Mexican artist/musician/inventor Ariel Guzik.

You'll find Guzik at Trinity Apse, a medieval church located down a close off the High Street. Last year its windows were entirely blacked out for Craig Coultard's film installation The Drummer And The Drone, so this year it's wonderful to see it bathed in light for Holoturian, which showcases the Mexican's ongoing project to communicate with dolphins and whales.

That's right, dolphins and whales. Guzik builds contraptions which are part exquisite steampunkery, part nuts-and-bolts engineering. He then lowers these contraptions into the sea, mostly off the northern coast of Mexico, and documents the resulting "expeditions".

The Holoturian is one such underwater vehicle. It hangs from a rusted iron gantry at one end of the church, beautifully wrought in wood, steel and brass and with a triangular front flap which sits open so its interior can be inspected. Inside is a cactus - emblematic of Guzik's homeland as well as the most waterless environment on earth - and a musical instrument resembling a zither. An ambient soundtrack echoes throughout the church and on the walls are exhibited drawings representing the other strand of Guzik's obsession with cetecean life: their imagined, underwater civilisations.

These, too, are beautifully wrought, line drawings of whales and dolphins annotated with curlicued symbols resembling some unknown and unknowable script. Two large cases hold "artefacts" from this civilization - fragments of bone, sea shells - as well as diagrammatic drawings and bits of machinery. Real? Who knows. The exhibition could do with a bit more in the way of explanation (and it isn't easy to find, either) but it's one of the EAF's most intriguing offerings.

Equally pleasing contributions to the commissions programme comes in the form of video pieces by Emma Finn and artist/musician Hanna Tuulikki. Finn shows Double Mountain in an unoccupied unit in the St James Centre, a playful piece which she narrates (as the mountain) and which features a cast of people dressed as (variously) fossils, tourists and scouts. It has some of the feel of an early 1980s pop video and you're encouraged to make paper aeroplanes from pages torn from The Observer's Book Of Aircraft and throw them at the screen.

Tuulikki's piece is Sing Sign: A Close Duet and it plays in a blacked-out upstairs room in historic Gladstone's Land on the High Street. Two screens face each other, one showing a costumed Tuulikki, the other a male collaborator. Around her neck is a long bib on which is printed a 1765 Edinburgh street map. The two performers face each other in an Edinburgh close - and they sing, a four-part duet which ping-pongs from screen to screen and whose "words" comes through choreographed hand gestures. Shot in black and white, it's beautiful, solemn and austere. Not unlike Edinburgh itself.

If it's colour you want, head for the Dovecot Gallery, another unsung hero on the Edinburgh scene. It's showing Aggregations, the first Scottish solo exhibition for Korean artist Kwang Young Chun, and Bernat Klein: A Life In Colour, a retrospective of the work of the textile designer and haute couture favourite.

Born in Serbia, Klein moved to Israel aged 18, was recruited by British intelligence during the war then lived the rest of his life in Selkirk where painted and made designs for fashion labels such as Coco Chanel and Christian Dior.

Grouped together, his simple oil on canvas abstracts have a compositional power they lack singly, but the show's pulsing heart is a series of five tapestries he made in 1972 in collaboration the Dovecot, then called the Edinburgh Tapestry Company. Adorned with great spurs of what looks like woollen impasto, they seem to pulse with life.

Equally impressive is Kwang Young Chun, who takes texts printed on mulberry paper, forms them into triangular parcels (facsimiles of the ones used to package Chinese medicines) then forms these into large, intricate, interwoven designs.

Some of the works are coloured, others are in shades of grey and black. Some are square, others round and fixed onto concave backings so they arc towards the viewer like satellite dishes. Some look like moonscapes, others like pixelated TV images, yet others like crystalline structures.

Dominating the gallery and hanging from the roof is a massive sphere, a sort of mulberry paper Death Star. Is it sculpture or tapestry? Is it, perhaps, conceptual art? After all, the texts themselves are often from books dealing with history or politics and in blacking them out or shading them, the artist is commenting on a subject common to much Chinese and Korean art: memory, both personal and collective. It's as effortlessly subtle as the work of Peter Kennard and Cat Phillipps is energetically shouty.

Elsewhere, honourable mentions should go to the four young artists involved in the Platform: 2015 show on Blair Street (particularly Ross Hamilton Frew); to Beatrice Gibbon for two films at the Collective Gallery on Calton Hill (the first time I've seen Minecraft feature in a work of video art); to Marvin Gaye Chetwynd and South African artist Kemang Wa Lehulere who have braved the frankly awful surrounds of the Old Royal High School to bring forth their EAF commissions; and to American artist Tara Donovan who has taken the prime spots at Jupiter Artland - the rooms by the cafe and the ballroom - for her exquisite and playful sculptural installations made from flattened slinkies, mylar (the stuff they use to manufacture helium balloons) and good old plastic cups - 600,000 of them.

Finally to English sculptor Phyllida Barlow and her aptly-named show Set. The title is a nod to one of her favourite materials - cement - and to the theatricality of works so large and intrusive that one of them has caused a blockage in the Fruitmarket Gallery stairwell you have to duck to avoid. Appropriately, that "piece" is called Blockade. The floor below is littered with more of the same, as if Blockade has shaken its innards into the downstairs space and not bothered to tidy up afterwards. I don't know what scrim is, but Barlow uses lots of it. Ditto pallets, wire mesh, timber, steel, cardboard, sand, plastic, plywood and "wadding". Three works titled Surveillance 1, 2 and 3 hanging from the ceiling in the cafeteria hint at some of her concerns: the urban environment, what we do in it, how we navigate it, how it confines us. In a festival which now has strong presence among the capital's other August offerings, it's an appropriately muscular place to end the tour.

The Edinburgh Art Festival runs until August 30

www.edinburghartfestival.com