In April, Nell Zink was on a brief trip to New York so she sat down and wrote the first draft of her next novel - her third - in 15 days.

"It is perfect," she says, with a whooping laugh. After the American novelist gave Nicotine - about a smoking cessation aid among other things - to her agent, it went for a six-figure advance. Again.

Zink's second book, Mislaid ("a subversive minstrel show sprung from an encyclopedic mind drunk on the Mad Hatter's tea," according to the Washington Post) also sold for "megabucks" in the wake of the literary sensation created last year by her debut book, the gloriously off-the-wall The Wallcreeper. This takes its title from a small crimson-winged bird that Zink has only ever seen in Innsbruck Zoo.

She had sold The Wallcreeper, for which she wrote a first draft in four days, to a tiny, independent publishing project, Dorothy, which specialises in work by or about women, for an advance of $300. Reviews for The Wallcreeper, with its madcap mix of sex, drugs, rock'n'roll - well, dubstep, actually - and eco-activism, were ecstatic. The New York Times called it "a very funny, very strange work of unhinged brilliance", while her bird-watching chum Jonathan Franzen - of whom more later - wrote "Her work instantly raises the possibility that the world is larger and stranger than the world you think you know."

With the six-figure sale of the satirical Mislaid, her income from writing multiplied each one of those 300 dollars for The Wallcreeper 666-fold, she tells me. She's since been profiled in the New Yorker - "friends were calling saying, 'It's a love letter!'" - and is now spoken of in the same breath as Don DeLillo, Nicholson Baker and Joseph Heller, while being hailed as "the new Kafka". Personally, I think she's unique, a literary one-off.

Zink left the US 18 years ago and lives in the small town of Bad Belzig, south-west of Berlin, where she shares a one-room apartment with her organic gardener boyfriend. Speaking from there she reveals the "bunch of money" she's earning for Nicotine. It's a great deal more than her Mislaid advance of £130,000. She asks me not to disclose the figure, but jokes that she's aspiring to join the middle-classes. It was not the million dollars her agent wanted. Next time, perhaps? "Yeah, that's exactly what my agent said!" she exclaims.

None of this would have happened and Zink would have carried on cheerfully writing in obscurity had she not sent a "well-written" note to Jonathan Franzen in response to a 2010 article he wrote for the New Yorker, about the illegal hunting of songbirds. He was intrigued by her stylish, bouncy, zingy prose and astonishing erudition.

They became pen-pals. He told her she should write fiction. She responded by sending him a novel she wrote for the Israeli writer Anvar Shats, whom she befriended when living in Tel Aviv with her second husband, the poet, composer and university lecturer Zohar Eitan. Soon Franzen was her biggest fan - she wrote The Wallcreeper for him - acting as her agent before his agent sold Mislaid, on the basis of the first draft, which Zink had written in four weeks. She then spent two years finishing it.

She has, though, been writing since childhood, after choosing "to [pitch] my tent outside the folds of humanity". Now 51, she's been homeless (by choice), worked as a bricklayer, a waitress, a secretary and a "noise band guitarist", published an animal-themed, post-punk fanzine in which rock musicians discussed their pets and, most recently, been a technical translator for drug companies.

Twice married, twice divorced, California-born Zink grew up unhappily and precociously in rural, post-segregation Virginia, where her father was a navy engineer. Her mother, a librarian before becoming a housewife "with literary pretensions" encouraged her daughter to write; then told her that nothing she wrote was good enough.

She tells me that her mother gave her the books that changed her life - "but in a negative way. When I was a teenage girl I was addicted to [romantic novelist] Georgette Heyer because my mother was a fan. Heyer's wonderful, but the relationship between men and women in those books, is not how the world works. Beautiful, bright ingenue, you will be discovered by perfect, older, experienced man. No! It is the Regency and she writes exquisitely, but I actively wish I had not been given Heyer's books. What was my mother doing, addling my brain in the hippie era of self-expression? Weird, really weird."

So, Zink is as much fun to talk to as she is to read. Which is presumably why her two novels are being published here simultaneously as a sunshine-yellow-bound box set. The Wallcreeper is dizzyingly fast-paced, narrated by Tiffany, who marries bird-watcher Stephen, a man she barely knows. They move to Switzerland, take other lovers and pursue different environmental causes, while living the avian lifestyle, "breeding and feeding". Zink has described it as "a tortured autobiography in impenetrable code... a really weird novel."

There's a lot of "hot sex" in The Wallcreeper, she acknowledges, then says: "There's not much sex in Mislaid, though. And, hey, none of it is pornographic. Although I do love to know, in real life, too, who's doing what with whom." Both novels skewer the institution of marriage mercilessly; Zink insists that she'll never marry again. "I'm not good at being trapped."

Punningly titled, Mislaid - "written in a state of fear that it might be mannered bulls***" - is a deliriously funny Shakespearean comedy of errors, set in Virginia in the 1960s. Teenage lesbian Peggy, and Lee, a gay male poet and professor, marry, have a son and a daughter; then Peggy runs away with her daughter, posing - on paper at least - as African Americans, despite being white. Indeed, cunning disguises and stunning surprises, to borrow Stephen Sondheim's phrase, abound.

"I wanted to write about racism and gender issues in the south when I was growing up in the 1960s and '70s, a forgotten time before the Old South receded. It was basically an apartheid regime, more like the '50s. So, yes, it's a political novel as is The Wallcreeper, which is about environmental issues," says Zink.

Virtually every reviewer has commented on Mislaid's Shakespearean plot twists. Despite her love of some of the plays, Zink has never read The Comedy Of Errors or Troilus And Cressida and claims that Mislaid is actually based on Viennese operetta, although a friend in Virginia tells her it's reminiscent of Gilbert and Sullivan. "Allegory maybe? I don't know what it is!"

Nonetheless, she's effortlessly adopted a Shakespearean "antic disposition" in the book. Probably because in childhood she read Hamlet, she told the New Yorker, "a million times". She once played the moody Dane in a boarding school production of Tom Stoppard's Rosenkrantz And Guildenstern Are Dead. She fell heavily after saying her three lines. For years, she bore the scars caused by her bra hooks piercing her back. This is what a conversation with Zink is like, filled with intellectually profound literary allusions, swooping effortlessly from gossip about shopping for a discounted new mattress to her days spent running, cycling, writing. "Being a novelist is such a good job," she enthuses, adding that this is perhaps the happiest time in her life.

Apart from one day, when she was just 20, standing by a roadside in Wales hitchhiking to Dublin. "I remember being there and feeling completely free. It was a moment of ecstatic happiness and freedom. I've never gone back, perhaps I ought to."

First though, she'll come to Scotland. Last December, Zink - a philosophy major at Virginia's William and Mary College, with a doctorate in media studies from the University of Tubingen, Germany - was interviewed by the Paris Review. She said: "Probably everybody assumes I only started living the dream after I got what Publishers Marketplace calls 'a good deal' for my novel Mislaid... the 'dream' for me, given my typically German lack of financial desperation, would be if somebody invited me to one of those literary festivals where you sleep in a comfy hotel somewhere interesting and speak English with people who are predisposed to be friendly."

She's about to live that dream, after being invited to appear at one of those literary festivals somewhere interesting, namely Edinburgh. "I know!" she exclaims. "I've a friend in Edinburgh and now I have another." She certainly does, I tell her, although she'll discover many people who are predisposed to be friendly towards a brilliant writer whose own story is more weird - Zink's favourite word - than any of her wild and wonderful fictions.

The Nell Zink Box Set: The Wallcreeper and Mislaid (Fourth Estate, £20). Nell Zink is at the Edinburgh International Book Festival on August 25, with novelist Kevin Maher.