In all honesty, what would life be ... without Abba in the soundtrack? Ha-ving the time of your li-ife. Is that the secret of Abba?

There was once a brilliant short story in 2000AD told from the point of view of an alien master race that was about to take over our planet. The aliens gloatingly described how they had infiltrated every household in the land, breeding in our cupboards, but quite unnoticed because the form they had taken was so innocuous. In the final frame their identity was revealed. They were ... wire coat hangers!

If Abba were members of an alien master race, they'd be those wire coat hangers. Ten minutes ago – or so it feels, if you grew up in the Seventies – they were those nice, but unexceptional, typical Eurovision one-hit wonders, with beards and blonde hair and twinky outfits, who won with their cheesy, toe-tapping glam number "Waterloo". Now, suddenly they're this extraordinary, über-dominant, global presence: critically unassailable, adored by everyone, still selling an annual three million albums decades after they disbanded, with the world's second-most valuable music catalogue after the Beatles and a new film out – Mamma Mia! The Movie – which is going to be enormous, based on a musical that has so far grossed $2bn.

And what I'm still struggling to understand is – how? It's not as though they ever had the cool and charisma of the Stones, or the versatility of David Bowie, or the range and depth of the Beatles. They never filled stadiums like Led Zeppelin did. If you had to make a list of bands who defined the Seventies zeitgeist, they wouldn't even make the top five.

Don't worry, this isn't going to be one of those pieces that goes "... but actually I think they're crap". I'd love to be able to write that piece – not least to wind up the idiots who dance to them at weddings, and the girls for whom a good Abba singalong goes hand in hand with foot spas, glasses of Chardonnay and walnut whips – but I'm not sure how you could. Take my personal favourite Abba song, "SOS". Just thinking about it sends my pulse racing, my spine tingling and my eyes welling with tears of nostalgia, melancholy and delight. Which is quite ridiculous really. I mean, I'm not gay or anything.

What I like – no, not like, worship – about the song is that it's got so many perfect moments. First, there's that grabby, descending intro – "ding-ding ding-ding dinnng, ding-ding ding-ding dinnng ... " – which has you salivating for the rest like Pavlov's dog. Then there's the gorgeous wistful bit where Agnetha comes in all fragile and pure: "Where are those happy days? They seem so hard to find..." Then there's the marvellous, roller-coaster adrenalin rush you get as the synthesisers accelerate you into a classic, slightly tinny (but none the worse for that) Abba wall-of-sound chorus, the sadness now rendered bearable by a change of key from minor to major. And then it's back to that intro, of which you can never get enough, and off we go all over again.

During the making of Mamma Mia!, the cast apparently used to joke about how when it was over they'd all have to go into Abba detox. But in the end, said Colin Firth on a TV documentary last week, it never happened. "Even when you think you're sick to death of them, after a few days you only have to hear the first few bars again and you start wiggling something," he said. His co-star Pierce Brosnan agreed: "It's infectious. However jaded your ear or your eye or your heart, you cannot help but sing along."

But why, exactly? To help me analyse it, I enlisted the expertise of Tim Rice, who once – before they were famous – employed the two girls Anni-Frid Lyngstad and Agnetha Fältskog in Swedish productions of Jesus Christ Superstar, and who wrote the musical Chess with Benny Andersson and Björn Ulvaeus.

One of the keys, he reckons, is the way Abba often like to combine jolly tunes with sad lyrics. "It's unbeatable," he says. "Super Trouper", for example – or rather "soo-pa-pa, troup-pa-pa" – sounds as if it ought to be about how fantastic it is to be a superstar, when it's actually about the loneliness and neediness of the performer. And the later into Abba's catalogue you go, of course, the more delightfully depressing their lyrics get as their marriages start to collapse and they pour their misery into their songs. Audiences dig this kind of cheery gloom.

Even so, I suggested to Rice, their lyrics do have quite a few rubbish moments. What about that clunky, "Thank you for the music, the songs I'm singing/ Thanks for all the joy they're bringing." Is there not something truly banal about that bringing/singing rhyme – though, of course it's not up there with Chris de Burgh's ineffable dance/romance rhyme in "Lady in Red" – not to mention the bit just afterwards where the singer asks, "In all honesty/ what would life be?"? Isn't it all a bit stilted? A bit foreign?

Ah, but that's exactly what makes them good, says Rice. "Because it's their second language, they come up with phrases that no Englishman could ever have written. Sometimes when you don't have the disadvantage of being able to worry too much about the language you're writing in, you throw caution to the wind and come up with moments of true genius."

He's a particular fan of the line, "No more ace to play", which isn't perfect colloquial English, but nonetheless nails the sentiment precisely – as Abba often do. "The emotions conveyed are very straightforward," says Rice. Which no doubt explains their appeal to so broad an audience, for many of whom English is not their first language either.

What Rice and I couldn't quite decide was the degree to which Abba had invented modern pop. There's no question that they legitimised Euro pop: before Abba, continental bands couldn't get arrested in Britain and the US; afterwards, we became much more accommodating, from Boney M all the way through to Scandi-pop outfits such as The Cardigans. But did they actually change the face of pop?

Well, possibly. Though Björn and Benny have claimed the Beatles as an influence, what's remarkable about their compositions is how dazzlingly original they are. No one has ever listened to an Abba song and gone: "That sounds a bit like..." Because it doesn't.

This may have a lot to do with Abba's being Scandinavian. In Britain and America, bands had – and still have – a huge reverence for tradition and an obsession with authenticity. Scandi-pop doesn't have to pay homage to old bluesmen, or agonise about keeping it real. It can just grab whatever sounds best and feels right. In the case of Abba – and most pop since – it's about combining a four-to-the-floor beat, with strong, instantly accessible melodies, and very clever, attention-grabbing hooks such as the one from "Gimme! Gimme! Gimme! (A Man After Midnight)" sampled by Madonna on her 2005 hit "Hung Up".

The fact that "Hung Up" was Madonna's biggest-selling single ever – it has sold 8.7 million and is the 43rd most successful song in music history – tells you all you need to know about the weapons-grade efficacy of Abba's hooks. This is not a point lost on their creators. In the Mamma Mia! documentary, Benny Andersson recalled the moment when he had received "a nice letter" from Madonna saying could she "please, please, please" borrow his riff. "She's a good artist," declared Andersson, in a tone which suggested, "and you'd bloody have to be if you're going to be allowed anywhere near our stuff".

Andersson's and Ulvaeus's canny business sense (they once avoided Sweden's 85 per cent top tax rate by investing in a bicycle-making business) and zealous guarding of their musical legacy is, no doubt, yet another reason for their endurance and global dominance. They seem to have understood, long before the rest of us, that Abba was never just a band. It was a back catalogue waiting to be exploited.

That's why the reasonable success Abba enjoyed as a band in the Seventies and early Eighties is as nothing to the huge success they've experienced in their afterlife, through countless tribute bands, through covers by Erasure, Westlife and Kylie, and now through Mamma Mia!

"Out of 140 songs, 60 or 70 are good and 20 are truly brilliant. For any songwriter, that's a pretty high batting average," says Rice.

So now you know. Abba are huge today because they wrote some of the best songs ever. Mystery solved.

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