Oliver originally studied to become a classroom music teacher at Aberdeen University and, in 2000, he moved to Glasgow, where he studied at the Royal Scottish Academy of Music and Drama with John Maxwell Geddes, gaining a Distinction for his Masters degree in 2002. He completed a PhD in composition in 2006 and has written works for the Paragon Ensemble, the National Youth Choir of Scotland, the Hebrides Ensemble, Psappha, Red Note, the Scottish Reed Trio, the BBCSSO, the National Youth Orchestra of Scotland, the New Music Players and the Royal Scottish National Orchestra.
In 2002, he received a silver medal from the Worshipful Company of Musicians in London and in 2004 he won the Mendelssohn Scholarship. Over the last few years, he has had works performed at festivals and venues around the world, with several broadcasts in Europe and Asia. He was nominated for a Royal Philharmonic Society Award in 2013 for Technophonia, and won a British Composer Award in 2018 for Microscopic Dances (working with Drake Music Scotland and NYOS). Recent endeavours include artist residencies in South Korea, a new work for the RSNO and collaborations with theatre-makers.