There’s a mad extravagance to “American Hustle” — the in-your-face ’70s furs and disco suits, the whipped-meringue hairstyles, the multilayered characters, the sprawling story. Every frame swells with a pushy, chaotic too-muchness, aburst with the grasping lunacy of American life. But even at two hours and 20 minutes, the movie doesn’t wear you down. It carries you along with heedless momentum, giddy and exhilarated at its all-American ambition and scam-artist confidence.

The plot of this exceptionally funny crime caper is jumbled but intentionally so, sliding through flash-forwards and -backs in a way calculated to keep us off balance. It concerns the cut-and-thrust collision of five people who want to make it big.

Pot-bellied comb-over king Irving Rosenfeld (Christian Bale, acting the part in bold, broad strokes) runs a few Bronx dry-cleaning stores as a front for his interests in art forgery and small-scale financial cons.

His ambitions rise when he partners with Sydney Prosser (cool, smoky-eyed Amy Adams), a New Mexico transplant savvy enough to know that an English accent, a phony title and a strategic deployment of leg and cleavage can hook bigger fish. Meanwhile, Irving’s being played like an accordion by his nut-log wife, Rosalyn (Jennifer Lawrence, living up to her sassy, over-revved character’s description as “the Picasso of passive-aggressive karate”).

Ambitious, naive FBI man Richie DiMaso (Bradley Cooper) snares Sydney in a sting and pressures her to recruit Irving for a high-profile case. Richie, hoping to make Watergate-style headlines, wants to nail a slew of top politicians. Irving arranges a deception involving a fake sheik and briefcases full of $100 bills. The first domino in line is Carmine Polito (Jeremy Renner), the beloved mayor of Camden, N.J. Polito wants to get north Jersey back on its feet with oceanside casinos and understands that a little seed money is necessary for such enterprises.

The good news is that Renner, a straight arrow who truly wants prosperity for his downtrodden constituents, is willing to facilitate a little honest graft. The bad news is that Bale, impressed by Renner’s integrity and guileless friendship, doesn’t want to double-cross him.

The entrapment scheme is just one element in a marathon of chicanery. Half the characters are trying to seduce the other half with influence or money or sex. Every time the cast is reshuffled in a new scene, the con games start over. Everyone begins every encounter looking for an edge, trying to out-think, out-negotiate, out-maneuver and generally upset the competition’s apple carts.

Innocent bystanders are swept up in the craziness. Louis C.K. has a splendid bit part as Cooper’s FBI boss, frazzled by his underling’s ever-escalating demands for private jets, multimillion-dollar wire transfers and enormous hotel suites. The comedically convoluted arguments skid around out of control until they’re so much pointless noise. And writer/director David O. Russell has a live-wire dream cast that can make nonstop conflict consistently entertaining.

The women are every bit the men’s equals, strong, independent masters of one-up-womanship. The faux-aristocratic Adams occupies every scene like a throne, while Lawrence pelts her fellow players with boomerangs and bombshells, firing off zingers with a rattlesnake lunge of her head.

They complete their co-stars. Cooper falls for Adams, Lawrence browbeats Bale, both guys are spineless cheats and neither woman knows what she wants. “American Hustle” is a screwball romance about the love of power. The stability of conventional marriage is out of the question and the most anyone hopes for is a temporary collaborative partnership and a big score. Viewers walk away the winners.