“Cher truly out-gayed herself with this one,” offered one LGBT website of Take It Like a Man’s delightfully double-entendre-laden, robot-voiced Euro-disco stomp with guest vocals from Scissor Sisters’ Jake Shears, little realising that an album of Abba covers was around the corner.

Firmly entrenched in the moneyspinning late-80s world of soft-rock balladry, After All teamed up Cher with former Chicago frontman Peter “Glory of Love” Cetera. Not as immediately effective as her best power ballads, it still has a certain emotional oomph.

You could perhaps tell that Sonny and Cher were bound not for rock stardom but for cabaret. Little Man is less like the boundary-breaking records at pop’s cutting edge in 1967 and more like the MOR that the people horrified by pop’s cutting edge turned to instead. Still, it’s a pretty charming song.

A flop album that essentially minted the AOR style that would lead to Cher’s resurgence five years later, I Paralyze’s title track is something else entirely – an intriguingly odd collaboration with former Shadow John Farrar, filled with weird chord changes and seasick-sounding brass.

Even if you hadn’t known that Sonny and Cher’s marriage was in trouble, you might have guessed something was wrong just on the basis of this bizarre but compelling single which opens with what sounds like its climax: a cacophonous minute of squealing guitars.

Compelling, bizarre … always on-trend, in 1978. Photograph: Harry Langdon/Getty Images

Not.com.mercial is an anomaly in Cher’s catalogue: an album of self-penned rock songs, from which this tribute to Kurt Cobain (yes) comes. She delivers it all with a conviction suggesting that, when it comes to the isolating effects of fame, she knows of what she speaks.

It is hard to decide which is the more improbable fact: that Cher ended up rerecording the solitary flop solo single released by former Ordinary Boys frontman turned reality TV star Preston, or that her version – a distorted bit of Daft Punk-y pop-house – really works. Winningly, she performed it live dressed as a vampire.

A one-off single, its eerie production the work of Phil Spector, A Woman’s Story is an extraordinary, bleak song. Something about Cher’s weary vocal cuts against the optimism of the chorus: the protagonist sounds doomed. Covered to considerable effect by Marc Almond.

Sonny and Cher’s movie debut, Good Times, was a disastrous flop: the first sign that a career that had once led them to have five songs in the US chart at the same time was hitting the buffers. But the soundtrack yielded this gem: booming pop sung with real affection by Cher.

In the list of improbable pop collaborations, Cher performing a song specially written for her by Prefab Sprout’s Paddy McAloon has to rank pretty high, but The Gunman works; a sumptuous, sophisticated ballad, decorated with vocoder backing vocals and early-70s soul touches.

The Kinks frontman Ray Davies’ epic mid-60s giveaway has been covered by everyone from Peggy Lee to Sia. Cher’s powerful take on the song, tucked away on her solo debut album, is the one that you suspect Chrissie Hynde of the Pretenders had in mind when they recorded it: the vocals are oddly similar.

In 1970 light-entertainment mode. Photograph: Kobal/Rex/Shutterstock

A much harder-sounding single than Cher was associated with at this stage in her career, Train of Thought’s blues/rock/soul/pop hybrid is an atypical gem from her early-70s oeuvre: proof her voice was more stylistically adaptable than her detractors believed.

A rare occasion when Cher’s music appeared to be offering a glimpse into her personal life – an emotive, soulfully sung depiction of a marriage on the rocks, released as her marriage to Sonny Bono faltered.

At this point, Sonny and Cher were light entertainers, which may be why Classified 1A went unreleased at the time. Written from the point of view of a soldier in Vietnam “dying in the mud”, and sung in tones of hoarse-voiced despair by Cher, it’s a ballad with more depth than their public image allowed.

It is not meant as faint praise to say that Cher can sing the most ridiculous songs with total sincerity, particularly when the results are as enjoyable as this preposterous load of black magic/infidelity/murder-themed hokum. A US No 1.

Such things are obviously relative, but Just Like Jesse James is a restrained single by Cher’s late-80s standards; an extremely well-polished bit of songwriting and a rare air-punch-inducing power ballad that resists the temptation to turn everything up to 11.

Sonny Bono was always a smarter, shrewder operator than the hippy garb and hapless public persona suggested. And there’s something impressively cynical about Sonny and Cher’s other big lasting hit, a view of the 60s in full swing, with one eyebrow knowingly raised.

Her 80s soft-rock incarnation. Photograph: Kobal/Rex/Shutterstock

It’s easy to see Cher’s album of Abba covers as an ultra-camp gag by a gay icon, but her version of One of Us is anything but knowing. She digs into the song’s dark heart, stripping away the original’s bouncy rhythm to produce an anguished depiction of romantic despair.

Cher as girl-group-styled ballad singer, with wall-of-sound arrangement and an adventurous, defiant Sonny Bono-penned song that won’t stay still, shifting and changing its time signature throughout. A lost epic.

The sound of the growing 60s counterculture scrubbed more or less clean for mass consumption, Sonny and Cher’s breakthrough hit remains irresistible, both in its sun-kissed depiction of youthful optimism and the sheer melodic force of its songwriting.

Cher capitalising on her song-stealing guest appearance on Meat Loaf’s Dead Ringer for Love with a big, irresistible guitar-driven ballad that Mr Loaf himself could have done. It was a hit for Laura Branigan a year before, but Cher’s reading obliterated the earlier version from the public memory.

Signed as a solo artist more as an extension of the Sonny and Cher brand than with any real musical direction, Cher’s early albums are an uneven mishmash of folk rock and Phil Spector-ish production. Occasionally they clicked, as on this cover, closer in tone to Bob Dylan’s sneery original than the Byrds’ sweeter reading.

Her career temporarily in the doldrums, Cher tried making a southern soul album, 3614 Jackson Highway, recorded in Memphis with backing musicians from Muscle Shoals. It wasn’t where her future lay, but it was surprisingly good. She sounds really powerful and in control here, on a cover of the Box Tops’ 1968 hit.

The kind of 80s soft-rock anthem that sounds inexplicably moving when you hear it on Magic FM in the back of a cab at 3am, the Bon Jovi-penned song heralded a musical renaissance for Cher after years focusing on her acting career.

Written for Cher and obviously playing on her exotic looks – half-Armenian, part-Cherokee – Half-Breed’s angry rebuke of racial intolerance is an entirely fantastic slice of tough early-70s pop: part thumping glam drums, part theatrical proto-disco strings.

An early hint of where Cher’s talents as a solo singer really lay, Bang Bang’s saga of first love turned sour sees her holding her own as the arrangement piles on the melodrama: flamenco-ish guitars, weeping Gypsy violin and a vaguely Russian-sounding interlude.

Cher should have made a better disco diva than she did, but her two albums for the Casablanca label were let down by weak material and a sense her heart wasn’t really in it. The title track of the second, however, is a triumph: funky, lushly arranged, pitched perfectly between melancholy yearning and sleazy one-night-stand-hunting lust.

In the early 70s. Photograph: Michael Ochs Archives/Getty Images

Her umpteenth artistic reinvention – this time as purveyor of pumping electronic dance-pop – was aided by an early example of Brian Higgins’ songwriting smarts: he went on to mastermind the career of Girls Aloud. In its prominent use of the then-new Auto-Tune audio processor as a vocal effect, Believe also has claim to be one of the most influential singles in modern pop.

Eighties power ballads could have been invented for Cher: not big on subtlety, grandiose to the point of seeming slightly camp and requiring a powerful voice to deliver them. A lot of her 1989 album, Heart of Stone, now seems very much of its time, but Diane Warren’s If I Could Turn Back Time is a song built to transcend its booming period production.

Gypsies, Tramps & Thieves.

Becoming unhip may have been the best thing that ever happened to Cher. She and her partner, Sonny Bono, had emerged in 1965 as exotic-looking harbingers of California’s hippy counterculture, but by 1968 they were hopelessly square, a monogamous couple who were anti-drugs: bummer. They ditched folk-rock and shifted towards Vegas: good news for Cher, whose voice was better suited to belting out showstoppers than grappling with Dylan’s Masters of War. Gypsies, Tramps & Thieves was the biggest showstopper of all, a gargantuan chorus tied to a fabulous example of the lost art of tale-telling songwriting – the pop song as picaresque short story. Over its course, she is variously angry, seductive, terrified and resigned: a great actor, though no one knew it yet.