Jesca Hoop, The Ballroom, Brighton

If you suspected, from her fairytale name, that Jesca Hoop was not entirely of this world, a few minutes in her company confirms it. A prodigious musical talent, her voice is Kate Bush meets Joni Mitchell, while her look is more Helena Bonham Carter complete with Victorian gothic aesthetic and bird's-nest hair.

Raised as a Mormon in north California, where she sang harmonies in church with her siblings, the free-spirited Hoop is now a self-confessed "black sheep" – mention of past lovers would suggest that she no longer practises her religion – and, after a stint as Tom Waits's childminder (no, I'm not making this up), is now a full-time musician and resident of Manchester.

It's no wonder, then, that Hoop is as much storyteller as singer, delighting us with a series of oddball digressions about her friends and family. The 35-year-old Hoop came relatively late to music, and as a result brings an emotional warmth and authentic life experience to her art.

Introducing "Angel Mom", she blithely tells us about her mother, a hardworking, clean-living woman who, a matter of days before her death from cancer, was persuaded to smoke marijuana by her children. Hoop had it shipped from a friend, and it arrived hidden in a jar of peanut butter. Prior to "Four Dreams" she recalls a brief plan to post her nocturnal visions on a blog. "But then I dreamt I slept with my sister, so that was the end of that," she says, her eyes rolling heavenwards. "We're all innocent in our dreams, right?"

Her songs are packed with similarly startling details. Literary in style and detail, they are closer to novellas, evoking the gothic songwriting style of Nick Cave, with their dark imagery, Biblical tenor and fascination for murder. "Tulip" talks from the perspective of a man, documenting his obsession with a flame-haired girl whom he marries and then drowns in a river on their wedding night. The hushed, sparse "Murder of Birds", which she sings on her album Hunting My Dress with her friend Guy Garvey, talks of spiders, cobras and demons as it recounts a mutually destructive love affair.

Tonight, Hoop's performance, which she airily introduces as "an evening of lyrics and melody", is a pared-down affair, with just her, her guitar and a backing singer named Becky. The sparseness suits her, casting a spotlight on her vocal prowess and the melodic complexity at the heart of the songs.

Musically, her magpie sensibilities lead her from earthy Americana to English madrigals via vocal ululations that come deep from her soul. Played live and stripped of accompaniment, the slightly mannered melodrama of her album settles into something a lot more natural.

Hoop's built-in charisma and unselfconsciousness is best illustrated when she attempts a brand new song about a child who longs to break a bone for the kudos it will bring. After the initial digression where she remembers her little brother playing in a pond while wearing a plaster cast, and emerging reeking of algae, she finally gets on with the job in hand. She stops and starts twice, mangles the lyrics but then renders the room silent and leaves us begging for more. It's both odd and utterly compelling. But that's Jesca Hoop all over.