You hear Roisin Murphy before she actually appears. Hidden in the wings, she intones the staccato verses of Royal T, a house-jazz mini-hit from 2010. She finally sidles into view, a dimly-lit figure wearing what could be antlers, but turns out to be a headpiece with stalks shooting out of the crown. It’s the first of half a dozen hats and as many costume changes, some of them impenetrably arty, such as the voluminous duvet/coat with origami-like folds. It’s not hard to see who Lady Gaga can thank for sartorial inspiration.

There’s an imagination at work here, and the clothes are just the visible layer. Murphy – formerly of electro-duo Moloko and now on her third solo album, Hairless Toys – is a clubber at heart, and much of her set replicates the sensory experience of bombardment by beats, bass and lights. The new songs sound gluey, eerily gummed-up: if Twin Peaks really does come back, here’s its soundtrack. Sometimes she drifts off on some inner-space voyage: the deep house track Jealousy becomes a 10-minute woozathon, her voice flipping in and out. The crowd respond by thrusting arms aloft on the densely packed floor. One couple somehow find space to pirouette.

But Murphy is no assembly-line diva. The Moloko songs Familiar Feeling and Pure Pleasure Seeker are served up with erratic tangents and jazzy tempo changes – there are moments when it seems she’s making it up on the spot. But the music always hangs together, and the wilder her flights, the more interesting she becomes. She takes an unexpected, and beautiful, swerve into Italian melodrama with Non Credere, from her 2014 Italian-language EP Mi Senti. Delivered unvarnished, with subtle guitar and keyboard backing, it shows Murphy as a passionate and powerful belter. She recently wondered why she’s never become a pop star. Perhaps it’s because she’s too odd, in the best way possible.

• At Trinity Centre, Bristol, 14 May. Box office: 0117-935 1200.