American showbiz eccentrics haven’t often made the leap to film biography, but there are some worthy of mention. Shock jock Howard Stern played himself in 1997’s relatively straight Private Parts, and two years later Jim Carrey won a Golden Globe for his part-tragic portrayal of oddball comedian Andy Kaufman in Man on the Moon.

‘Weird Al’ Yankovic is cut from similar left-field cloth to the above subjects. An accordion-playing parodist whose ’80s rewrites of hits by Madonna (Like a Surgeon), Michael Jackson (Eat It) and Queen (Another One Rides the Bus) found favour with the emerging MTV generation, he carved out a lengthy career that has seen him rack up album sales in excess of 12 million.

This, however, is far from a faithful depiction of the comic’s life, but instead offers an alternative history, co-written by director Eric Appel and Yankovic himself, with its tongue firmly in cheek. Here, the young Al has a miserable home life with parents outraged by his passion for changing the words to songs that already exist (“What you’re doing is confusing – and evil!” yells his father), and falls foul of heavy-handed law enforcement intent on breaking up illicit polka parties.

But when the grown-up Al (Daniel Radcliffe) finds like-minded souls, including a mentor in the form of famed novelty record radio DJ Dr Demento (Rainn Wilson), his rise to superstardom is lightning fast. Before long, he’s living it up in a mansion with no less than four Jacuzzis, breaking The Beatles’ record for the most songs in the American Top 10, and declining an invitation from Queen to join them on stage at Live Aid.

Sounds outlandish, doesn’t it? We’re not done yet. Opting to ditch parodies and focus on entirely original material, Yankovic is stunned when his first, supposedly, completely self-penned smash Eat It is itself parodied by Michael Jackson as Beat It (“Is it about eggs?” he asks). But his world falls apart after embarking on a tempestuous love affair with a coldly ambitious and manipulative Madonna (Evan Rachel Wood), and he’s forced into vigilante action to battle notorious drug lord Pablo Escobar.

The laughs come thick and fast, although in more episodic fashion than as part of a robust narrative. Several scenes feel like standalone sketches, like when Al attends a bizarre, celeb-packed pool party where the other guests include Salvador Dali, Alice Cooper and Andy Warhol – the latter, played by late night talk show host Conan O’Brien, is deliciously dismissive of the new kid on the block: “I give him 15 minutes,” he deadpans.