Other than the Segway in the foyer and the accordion by the fireplace, “Weird Al” Yankovic’s house is not so weird. A modernist, multilevel compound steep in the Hollywood Hills, it blends with its ornately anonymous neighbors.

A kumquat tree by the front gate is studded with small orange fruit. Up a flight of concrete stairs, a swimming pool lies shaded beneath overhanging stories. Another flight up and inside, Yankovic’s living room is bright, white-walled and -tiled, hung with colorful but subdued abstract art, vaulted floor-to-ceiling windows giving a long, smoggy view westward to the Pacific. On his coffee table, surrounded by glass art and stacks of family photos, sits the book Bird by photographer Andrew Zuckerman.

In the ninety minutes I talked with Yankovic on a mild April morning, the accordion went unplayed, but trying the Segway, he declared, came with being invited to his home: “The indoctrination.” I took it for a short, swerving ride across the living room.

In this setting Yankovic himself was rather genteel, articulate, and light. He answered the door barefoot, in Diesel jeans and a floral-print polo, long, angular face maybe a day unshaven, long, kinky hair past his shoulders. His voice revealed little trace of the goony croon of joke-pop classics like “Like a Surgeon” or “Eat It.” Yankovic—who’s earned a degree in architecture from Cal Poly University, a handful of platinum records, and three Grammy Awards—started our conversation with an almost-formal tone but eventually relaxed into a less-restrained tenor.

This is a man who for thirty years has made a living—a good one—by out-farcing the farce that is popular music. Yankovic is so associated with the pop-music parody that a fan-managed website, The Not Al Page, exists to correct falsely attributed songs (125 and counting).

Yankovic’s most recent album was a greatest-hits package released late last year; preceding it was a download-only EP highlighted by the Doors-inspired sendup “Craigslist” (“You got a ’65 / Chevy Malibu / With automatic drive / Custom paint job, too / I’ll trade you for my old wheelbarrow / And a slightly used sombrero / And I’ll even throw in a stapler, if you insist / …Craigslist!”). The album before that, 2006’s Straight Outta Lynwood, was Yankovic’s twelfth and his first turn on the Billboard Top 10. Last year he debuted a multimedia, celeb-studded educational film, Al’s Brain in 3-D, at the Orange County Fair and the Puyallup Fair, outside Seattle. It ran again this year and once again attracted record crowds.

Yankovic’s annual summer tour runs through September and in...