Last year's album from The Eccentronic Research Council, Johnny Rocket, Narcissist & Music Machine… I’m Your Biggest Fan, was narrated by the fictional stalker of a fictional rock star in a fictional band in a fictional northern town. That fictional band was The Moonlandingz, and the album included one song by them – the rampant belter Sweet Saturn Mine. They have since stepped into the real-ish world with a five-date UK tour and an album that's due early next year.

They called it the Ultimate Realism tour – and as far as I can tell they're taking the piss but they also absolutely mean everything they say and do. Tonight is the last show, at Oslo in Hackney, and there is rage and exhaustion mixed all together with energy and pomp and chaos and ace music. It's an exquisite balance - cosmic and batshit, authenticity and pantomime - it reminds me of something physicist Richard Feynman said: “The world is a dynamic mess of jiggling things if you look at it right.”

Two of The ERC – Sheffield's Dean Honer and Adrian Flanagan – are the foundation of The Moonlandingz, with ERC cohorts brought in on bass, drums and guitar. The lead singer is still Fat White Family's Lias Saoudi, though FWF's Saul (who's also part of The Moonlandingz) isn't here. And, in a stroke of genius, the stalker (played by Maxine Peake on the album) seems to have joined the band: we now have Rebecca Taylor fronting the show alongside Saoudi, and it is weirdly, brilliantly fascinating, not least because there's no clear indication of who's got the upper hand.

Saoudi is the eye of the storm, the absolute centre of attention – a charisma triumvirate of Beyoncé, Iggy Pop and Elvis would struggle to upstage him – and tonight his Johnny Rocket persona is dressed in boxer shorts and a red leather tassled jacket. He's got CUNT written in lipstick across his forehead, and he's wearing his signature bread bangles (made by punching through half a loaf of Warburtons). Taylor prowls, hisses and sneers around him, fixing eyes with the audience, leering and licking her lips, blonde hair on her face and leopard print shirt half undone, lipstick smeared across her chin, like some young Joe Elliott goddess after an especially sordid and invigorating night out. Saoudi leans in to her occasionally, cuddles, snuggles, offers comfort, gives her orders (which she responds to in a Gollum voice: “Yes, Master”), then he gets on his hands and knees and makes some attempt at a second birth through her legs. They fall down together, singing and snarling. Mairead O'Connor on guitar is icy-faced, spooked and glamorous, like a David Lynch heroine. Honer and Flanagan stand at each side of the stage, behind synths and organs, in their hats and dark glasses, like South Yorkshire svengali bookends.

They play the whole album, and it is ace. Right from the first song, 'Vessels', there's filthy motorik stomp, grabby synth riffs, soaring swirling B-movie sci-fi electronics and just a lot of very very good songwriting. Saoudi's voice is sad and sinister, fuzzy; often he's screeching and yowling, occasionally he has a touch of Vic Reeves' club style or the R White's secret lemonade drinker, then there's that arch Nick Cave spookiness, then he is plaintive, desperate, appalled and fascinated by human proclivities. The lyrics dig in to all these qualities and more. As with Fat White Family, there's plenty of prodding at open wounds and a disdain for social propriety. 'Lufthanza Man', for example, is a brilliant singalong tune about the Germanwings pilot who crashed his plane into the Alps on purpose last year, killing 150 passengers and crew (“Can you feel that mountain calling?” it goes. “Can you feel life dissipating… into the blue, into the blue?”); and, as with Fat White Family, it manages to look straight at the mindboggling horror of it with a kind of sweet melancholy, as well as an excellent scuzzy riff that sounds a bit like Wings' 'Live And Let Die' and retro space-travel beeps and swooshes.

Oscar Wilde said, “One must have a heart of stone to read the death of Little Nell without laughing,” and I think he would have liked The Moonlandingz and their embrace of confusing horrible-wonderful reality. Those details and delicate balances might be lost when you're one of almost 400 people watching this blasting, joyful and often demented band, but the stupid-genius energy at work here is always in full effect. They're like Devo or The Monks – juvenile and raging – with added Northern sarky pomp. 'Neuf De Pape' (named for the wine they got used to while recording at Sean Lennon's studio, and delighting in the playful propulsiveness of those words) is stomping, chanting daftness; '40,000 Years Of Job Club' is livid and exhausted, a Wham Rap! for Brexit Britain, trapped in the shitty rigmarole of signing on, looking keen and feeling second best to all those hard-working families we keep hearing so much about. It's funny too, laughing with rage, with camp theatrics as well as glam chugs and swirling disco sounds.

The final song is the jittering, panting, squelching 'Man In Me Lyfe', from last year's EP (“for my best friend, who isn't here,” says Lias). The crowd has been rapt the whole gig, singing, yelling, swooning, moshing. Now Rebecca Taylor begins to pull women out from the front of the stage, one at a time. She lifts them up, wraps their legs around her waist, leans them back and then propels them into the crowd so they surf, laughing and singing, across the room. She does it once, twice, three, four times. Then the bloke who's been the most lairy in the moshpit all night clambers on to the stage and launches himself into the crowd, and falls straight to the floor. All this, of course, is among the lovely chaos of the last song. Mairead is smiling now, Dean Honer remains impassive, Adrian Flanagan is smoking a fag and surveying the excellence and the mess. I trust he's pleased with himself. They are taking so much territory here – fantasy! reality! sex! rage! fear! fun! horror! - and it's so exciting, and the songs are so good.

The Moonlandingz' debut album is out early next year on Transgressive Records. All photos courtesy of Holly Whitaker whose work can be found here