Asked what was the plan for her show at The Kate next Thursday night, Nellie McKay paused. Dramatically.

Her reply was, well, evasive. “I’m bringing my dog and a wild woodsman,” the irrepressible 35-year-old said with a grin in her voice during a recent telephone interview from her studio in Pennsylvania. “Also my ukulele and probably a harp.”

Which is to say that eclectic is not a word that can begin to contain the exhaustively inventive, genre-bending McKay (it rhymes with “not shy”).

Rolling Stone described the acclaimed New York musicmaker as “a renegade songwriter with an ultraflexible Great American sensibility.” She’s also an ivory-tickling, ukulele-slinging chanteuse, with a voice that, as Beatles historian Matt Hurwitz put it, “easily places the listener in a smoky nightclub at two in the morning surrounded by empty martini glasses.”

Not to mention an iconoclast from the very start of her career.

At 21, she was in the midst of recording her debut album, “Get Away From Me,” a tart answer to Norah Jones’s smash “Come Away With Me.” Her contract called for 13 songs. McKay wanted a double album, lobbying her label with a PowerPoint slideshow and bottles of wine.

The New York Times lauded the 2004 release—all 18 tracks of it—as “a tour de force from a sly, articulate musician who sounds comfortable in any era.” The Washington Post declared that “this supremely gifted, charming, and darkly funny New York oddball has all the makings of the first great singer-songwriter of the young century.”

That the Philadelphia Daily News called it not just “brave, brash, brilliant” but also “maybe a little batty” is no wonder, arguably, in light of her unconventional upbringing.

Born in London to an American actress and British director who split soon after, she settled in Harlem, where her mother kept her surrounded by musicians and artists and everyone from a “gay opera singer from El Paso” to a “folk singer who was a closet Republican.”

At 10, the two crossed the country in a VW van crowded with their dog and nine cats to Olympia, Washington.

“Not the most artsy place,” said the woman who, the New York Times reported, “can quote the radical feminist Shulamith Firestone and Doris Day in the same breath.”

From there, it was onto rural Pennsylvania. At 16, she moved back to New York, enrolling at the Manhattan School of Music to study jazz voice. After a few years, she dropped out. “I was always wanting to be going out and auditioning for something and getting it,” she said.

That was precisely what she did, following the critical success of “Get Away From Me” with a celebrated Broadway debut at 24 co-starring with Alan Cumming and Cyndi Lauper in “The Threepenny Opera.” A year later, she appeared on the big screen as the sister of Hilary Swank in the 2007 romance “P.S. I Love You” and then, in 2011, as a street musician opposite Philippe Quint in “Downtown Express.”

“It’s a relief,” said McKay, of her forays into acting. “I don’t want to be myself. I have to live with her.”

That’s also true of her series of tribute shows, evidently. Her musical extravaganza, “I Want to Live!” was based on the life of murderer Barbara Graham, the third woman executed in the gas chamber at San Quentin in 1955. (“Barbara knew how to have a good time,” she said.) Another show, “Silent Spring – It’s Not Nice to Fool Mother Nature,” draws upon the life of conservationist and writer Rachel Carson.

Still, whether she’ll be doing her take on June Rover, as she referred to the late comedian in her latest musical biography, or Katharine Hepburn, in whose voice she answered the phone, or torch-singing cabaret, or rapping, or scatting, as she does on a track of her upcoming release, “Sister Orchid,” or all of the above, there will be a plan.

After all, “it’s important to make plans so you can break away from them,” she said, without the slightest pause.