I don’t know whether to call this a comedy or an oddity. I’d love to report that “The Imaginarium of Doctor Parnassus” is a work of renegade genius. Alas, it’s a minor film, memorable largely as the farewell of Heath Ledger, who died when his scenes were only half-completed.

Ledger plays Tony Liar, a shady businessman saved from suicide by Dr. Parnassus’ wandering theater troupe. Tony, who may be grateful or may need to lie low, joins “The Imaginarium,” a cheesy horse-drawn sideshow caravan. Parnassus (Christopher Plummer) is a mystic who ushers onlookers through a cheap Mylar looking glass and into a world reflecting their own imaginations. For a hostile, drunken club boy, it’s an inferno of honky-tonk bars. For a fashionable matron, it’s a vapid wonderland of giant high heels and beach ball-sized pearls.

Director Terry Gilliam, who began as Monty Python’s animator, has the most uncanny visual imagination in feature films today – and the most slapdash story sense. Like all of Gilliam’s movies (including the classics “Time Bandits,” “Brazil” and “The Fisher King”), his latest cocoons us in surreal imagery, pictorial wit and anything-goes dream logic.

It says something about the ramshackle nature of this yarn that Ledger’s disappearance midstream doesn’t capsize it. His sequences segue into fantasy scenes in which his role is played by Johnny Depp, Jude Law and Colin Farrell. By that point, you can only shrug and say, “OK, whatever.”

“This world we live in is full of enchantment for those with eyes to see it,” announces Parnassus’ young carnival barker, Anton (Andrew Garfield). Unfortunately, almost everyone on either side of the footlights is blinkered by materialism, indifference, wrath or envy.

Parnassus’ sidekick, Percy (Verne Troyer), pesters the old man for losing his moral bearings, berating him like a sarcastic Jiminy Cricket. The doctor’s nubile daughter, Valentina (owl-faced supermodel Lily Cole), is impatient for a normal life away from her frequently drunken dad. Parnassus wants to keep her close; a millennium ago he made a pact with the devil (Tom Waits), eternal life in trade for his firstborn daughter, and it’s time to pay up.

Gilliam has contradictory goals – visual phantasmagoria and social-theological satire – and the tale goes wherever the wind blows. “Parnassus” offers a critique of just about everyone with a vested interest in the status quo.

Tony Liar, is a harsh mockery of slippery former Prime Minister Tony Blair. Gilliam loves undercutting our expectations: The guy we want to be the hero disappoints us, the wise old sage is revealed to be clueless, and Lucifer turns out to have a solid moral code. Interesting concepts, but the characters are so thin that they seem inconsistent rather than complex.

Ledger supplies a rococo performance, slipping between accents and gesturing theatrically, while each of his understudies veers off in his own direction. Farrell is onscreen longest and fares best, but none has more depth than the paper cutouts Gilliam shuffled around in his old Python animations.

Like Gilliam’s recent films (“Fear & Loathing in Las Vegas,” “The Brothers Grimm” and “Tideland”), this is a gorgeously wrapped gift box without much inside.