For the song “A Hard Day’s Night,” The Beatles set to music a scene of themselves running from screaming fans. In the video for “Phantom Punch,” Sondre Lerche (pronounced son-druh lair-key) and his band also run in a pack away from strangers — however, they are running in a bizarre dream world, not London; and their pursuers are not teen fans, but people wearing horse heads.

It would be unwise to consider this a coincidence. Lerche’s influences range from Cole Porter, a devastatingly witty and urbane songwriter from the 1920s to the 1950s, to Burt Bachrach, whom you probably know from his cameo in “Austin Powers,” to Elvis Costello, with whom Lerche recently toured. All of these influences might bog a lesser musician down in slavish recreation, but Lerche assimilates them all in his own offbeat style and humor — like mixing The Beatles with horse heads.

Most importantly, he writes fun music. He overlays catchy hooks with charming, offbeat lyrics (sometimes it’s hard to tell if he’s being goofy or if it’s a crack in his English) and delivered with guileless, heart-on-his-sleeve phrasing. All of this makes you want to dance around in your underwear playing air guitar and singing into your hairbrush. “Phantom Punch” (2007), his fourth and newest full-length album (after “Faces Down” (2002), “Two Way Monologue” (2004) and “Duper Sessions” (2006), for the last of which he slicked his hair back and played crooner) brings the sweet guitar licks and lilting vocals that have endeared Lerche to his fans. But on the title track, he incorporates prickly electric guitar riffs and a dance-club beat — innovations for his style that don’t sound as if they should work with his previously symphonic, layered melodies but nevertheless do.

The layers have become crunchier and rougher, but they haven’t gone anywhere. Lerche’s music offers the sheer sonic pleasure of discovery — discovering a new quirk, a new clever touch with every listening. “Phantom Punch” brings aggressive, hard-driving rock to his previous layered melodies but retains their complexity. Just as every song offers unexpected touches and twists, Lerche’s music grows and changes with every new album, making him a fascinating and addictive songwriter to listen to within each song and to watch throughout his career.