HELLO, DOLLY! Nellie McKay’s subversive streak belies her retro affectations.

The natives were restless by the time Nellie McKay scurried on stage at the Paradise a week ago Tuesday, all dolled up in a vintage coral chiffon dress and sparkly silver slippers, and carrying a messy stack of notebooks full of lyrics and sheet music. She’d gotten lost on her way to the club, she apologized, and was an hour late. But all hard feelings were set aside as she sat at the piano, shuffled through some papers, and began a beguiling solo set that was as playful as it was potent.

McKay is an odd duck — a true musical eccentric who honed her jazzy piano chops at the Manhattan School of Music before embarking on a solo career as a whip-smart, saucy-tongued solo artist with a taste for everything from Broadway musicals to Brill Building pop to classic cabaret. Despite being well-schooled enough to star in a Broadway production of The Threepenny Opera, she isn’t a straight revivalist like Jane Monheit and Diana Krall, or as straightforwardly trad as a Norah Jones. Although she looks, and often sounds, as if she’d been plucked outta the ’50s, she has a subversive streak à la Tori Amos or even Liz Phair that’s thoroughly modern.

In front of a standing-room-only cabaret-style seated crowd at the Paradise, McKay could easily have charmed her way through the entire set with her torch-singing chanteuse routine. But she’s too sharp for that. The romance in “There You Are in Me,” for example, is shot through with cutting verbiage like “Everyone you meet secures a wretched seat within your memory/Wipe their filthy feet upon the yearning of your soul” — the very stuff that’s earned her comparisons to Randy Newman. Even the novelty number “Ding Dong,” with its ringing-doorbell refrain, offered more than just laughs, as McKay wound her terse voice around the lines “Do you have a little time/Would you like to feel sublime/Run away and never stop/Chop your head off/Be a lighter person/Brighter person/Nicer . . . But you’ve heard it all before.” Perhaps we all had, but never quite like that.