Unique, wacky and more than a little bit mad, Michael Clark's triple bill at the Barbican will leave you speechless, if a little frazzled. Co-commissioned by the Barbican, the works Michael Clark Company present do not have individual names, but form three parts of a whole. This is an upgrade of the double bill Clark presented in Autumn 2012, which consisted of two diametrically opposed halves and has been likened to two sides of a vinyl record. The record analogy is extremely apt for describing Clark's choreography: it's astounding how closely music and movement are tied together in All Three at Once. This bold, unapologetic triple bill bombards the brain from all directions: I can safely say I have never before seen anything like it.

As a lone dancer was lowered from the ceiling against a glowing bright-green backdrop toward a bare stage, I had no idea what I was in for. When the lyrics of Scritti Politti's smooth synth-pop The Boom Boom Bap kicked in, my first impression was how impeccably timed the choreography was: every movement was perfectly placed to coincide with a song lyric.

The movement had the overall appearance of simplicity – one section of the initial piece looked almost like warm-up exercises in a ballet class, legs swinging like ticking metronomes. Yet the clean lines and geometric shapes of Clark's choreography make it appear simpler than it is. On one occasion, two dancers backed onto the stage, feet shuffling quickly along the diagonal as their backs arched and pelvises oscillated between one jaunty extreme and the other. One female dancer communicated with another using hand signals, provoking an aggressive two-fingers-up reaction from a male dancer between them. A handstand led one female dancer into a duet with another on the floor, the pair's legs continually crossing and un-crossing. Suddenly, all six dancers were on stage, side-stepping and switching places within a straight line, perpendicular to the audience, as if imitating the heavy swing of a Newton's cradle. They moved in two trios, so that they were never fully visible at the same time, maintaining impeccable timing to a complex rhythm, even after the final notes from Scritti Politti had faded to nothing.

Clark's choreography maintains sharp, geometric lines throughout the second piece of the evening, which was danced to the imposing sounds of Public Image Ltd's Albatross, New York Dolls' Looking for a Kiss and New York by the Sex Pistols. The dancers performed subtly odd, angular movements – a sideways tilt of the head as one dancer pivoted on the spot, an uneven limping gait across the stage, and a downward focus of the eyes – which gave the choreography an element of strangeness. During the crescendo of Albatross, all six dancers travelled across the stage, each one a few steps ahead of the next, following a specific pattern of quick feet, pivots and closely observed rhythms. The sounds of the Sex Pistols crashed in, and the dancers performed to the exact rhythms of this specific recording with astounding timing. All the various rhythms of the song – vocal line, guitar and drums – were danced simultaneously, presenting almost too many concurrent actions for the audience to take in.

The final piece of the evening was danced entirely to music by Jarvis Cocker's bands, Pulp and Relaxed Muscle. The first section captured the angsty frustration and sexual tension of Pulp's F.E.E.L.I.N.G.C.A.L.L.E.D.L.O.V.E. in various moments: one dancer would lie face-down, their hands beneath their hips, and draw their pelvis upward while arching their back. Coinciding with Cocker's breathy voice-over, this movement provoked a feeling of discomfort. Various dancers lay spread-eagle on the floor, legs wide open toward the audience, their legs and crotch the only visible section of their body. The sexual nature of the choreography continued to build throughout the last piece. A highly sexualised sequence featuring a mirror-topped stool was repeated in canon by each of the three female dancers, which included angular pelvic movements, thrusting the hips back and forth, and the manipulation of the stool between their legs.

Clark's triple creation is innovative, quirky and challenging for both the audience and performers. The precise and deliberate choreography tends to favour unnatural movements, and requires a huge degree of control. The six dancers, Harry Alexander, Julie Cunningham, Melissa Hetherington, Oxana Panchenko, Daniel Squire and Benjamin Warbis, performed well, although at times the choreography seemed a little beyond their capacity, as strain was clearly visible.

The audience was challenged time and again by the loud eclectic choice of music, brightly coloured lighting, the dancers' full-length unitards in bold designs and luminous colours, and finally a projected film by Clark and Charles Atlas, which was equally mad and eye-catching, and had the tendency to divert attention away from the dancing. At times it was almost impossible to work out where to look – I felt I was constantly missing things because my brain was being overloaded with a plethora of music, colour and movement – but it seems as though Clark is deliberately challenging his audience to engage with, and to fail to define, his piece. Having had my senses bombarded, I left the Barbican feeling utterly astounded and quite speechless. The feeling was mutual among the audience, who sat in stunned silence a few moments before enthusiastic applause broke out. His work is almost impossible to describe, but Michael Clark is definitely a choreographer to watch and keep an eye on.

Michael Clark Company, at Barbican TheatreCatherine Sutherland reviews Michael Clark Company's new triple bill at the Barbican Theatre