The burnt-out rock star has been a movie staple for almost four decades, like a post-Altamont hangover that never ends. Ever since Jimi and Janis checked out of the Hotel California, Syd got his sick note from Pink Floyd and Elvis left the building, filmmakers have seized on the alluring fantasy of pop stardom as a pathological condition, usually leading to a glamorous and potentially lethal kind of post-traumatic stress disorder.

From Jagger's self-exiled subterranean sex-god casualty in Performance and Dylan's grizzled elder statesman in Hearts Of Fire, to the staged death of a Bowie-sized megastar in Velvet Goldmine and the return of a Syd-inspired ghost in Still Crazy, via David Essex suffering toxic fame overload in Stardust and Michael Pitt's doomed Kurt-a-like in Last Days, the cinema simply loves pop fame as Icarus myth. Rock 'n' roll suicide meets messianic resurrection.

Now the Italian director Paolo Sorrentino makes his contribution to this long-running genre with This Must Be The Place: a highly eccentric mix of post-punk musical, revenge drama and tragicomic road movie. Named after a classic Talking Heads song, Sorrentino's first English-language work stars Sean Penn as a 50-year-old retired rocker confined to listless exile in his Dublin mansion.

Dressed in full Robert Smith goth-drag, Penn's Cheyenne is a mentally fragile wreck given to pained musings such as "why is Lady Gaga?" (sic). He's also emotionally and creatively frozen by personal tragedy until a much bigger catastrophe – the Holocaust – looms back into his life with his father's death. Following the New York funeral, he embarks on a mission across America to avenge his late father against the former concentration camp guard who once humiliated him.

The real-life rock hinterland to Sean Penn's extraordinary performance goes deeper than his Edward Scissorhands make-up. Sorrentino admits Cheyenne's look was a straight steal from The Cure frontman, partly because it neatly encapsulates the film's theme of an infantilised child-man still locked in adolescent habits deep into middle age. But the Native American name pays elliptical homage to another post-punk goth icon, Siouxsie Sioux, while Penn's squeaky voice and zoned-out state suggest some bizarre, parallel universe hybrid of Michael Jackson and Ozzy Osbourne. With just a hint of Chris Griffin from Family Guy too.

Beyond these obvious echoes, the heavy hand of Bono can also be detected just outside the frame of Sorrentino's camera. Most obviously, the U2 singer's 20-year-old daughter Eve Hewson co-stars in a supporting role, and does a perfectly decent job. His childhood pal and occasional musical partner Gavin Friday also gets a song and a namecheck on the soundtrack, which we can only assume is happy coincidence. Penn and Bono are friends, inevitably – the singer hosted the actor's 50th birthday party during the Dublin shoot. Even as Cheyenne shuffles around his blinged-up Dublin mansion, half art gallery and half colonial castle, Bono is very much the elephant not in the room.

Wherever you stand on Bono's music or charity activism, his track record in cinema is dismal. At its most gratingly whimsical, This Must Be The Place summons the scary ghost of 2001's notorious turkey The Million Dollar Hotel, a career-staining low for both the celebrated German director Wim Wenders and his rock-superstar buddy, who conceived the story during a U2 video shoot. This was arguably the ultimate example of the myth of the burned-out rock star elevated into a grotesquely self-indulgent abortion that even the film's producer and co-star, Mel Gibson, later dismissed as "boring as a dog's ass". That's right. Mel Gibson.

The Curse of Bono and its demonstrable effect on Wenders' career decline over the last 15 years offers filmmakers a warning from history, but not one that Sorrentino has heeded. This Must Be The Place borrows heavily from the German director's American road movies, explicitly his highly regarded 1984 drama Paris, Texas. Each picture involves a guilt-haunted man making a lonely quest across epic American landscapes to unlock family secrets and settle scores. Harry Dean Stanton appears in both.

But at its worst, Sorrentino's film has more in common with late-period Wenderlust: banal exercises in jukebox Americana like Don't Come Knocking, the little-seen 2005 'sequel' to Paris, Texas, which deploy grand landscapes and windy sentimentality as poor substitutes for emotional or political substance. Diners and gas stations, billboards and motels, lost highways and widescreen vistas: broad as an ocean, but shallow as a puddle. Sorrentino has admitted he shot the US like an awestruck European tourist: "American places are a dream and, when you find yourself in them, they don't become real but continue to become a dream."

Of course, neither Sorrentino nor Wenders are the first European directors to rashly take on the Big Subject of America only to find themselves lost in translation. For every Sunset Boulevard there is a Showgirls; for every novelistic classic such as Chinatown, there are countless portentous sermons like Zabriskie Point. Fortunately, This Must Be The Place boasts several trump cards to help redeem its fanciful Euro-snob tone. Firstly, Penn's eccentric performance is a bold comic transformation on a par with prime Alec Guinness or Peter Sellers, breathing soul and depth into an otherwise potentially risible caricature. The unassailable Frances McDormand, who plays Cheyenne's long-suffering wife, and the solid screen veteran Judd Hirsch, as his Nazi-hunting mentor, also lend much-needed grit and gravitas to Sorrentino's meandering tourist reveries.

David Byrne's involvement is another coup, having inspired the film's title with the much-loved Talking Heads tune 'This Must Be The Place (Naive Melody)', which he performs in a bravura, gravity-defying concert sequence. The egghead pop professor also plays himself in a brief dramatic scene and co-wrote five songs for the soundtrack with Will Oldham, an unlikely pairing which produces some agreeably warm-hearted country-folk ballads. Perhaps more significantly, Byrne's presence provides a kind of alibi for the movie's whimsical excesses, since the singer's own brand of post-modern playfulness has always been backed up with sharp intellect and critical subtext. With the perennially boyish Peter Pan of post-punk pop on board, we are more inclined to give Sorrentino's faux-naïf fairy tale the benefit of the doubt.

That said, This Must Be The Place ends on an oddly anticlimactic note involving a silly act of poetic justice in a vast, snowy landscape. Again, the ghost of Wenders hovers in this frictionless fantasy of actions without consequences, revenge without pain. Further proof that travelling hopefully is often better than arriving. But thanks to a great cast, some fine music and one of the most audaciously weird star performances ever committed to screen, Sorrentino's flawed rock 'n' roll road movie is still a journey worth taking.