Oliver is in demand as a broadcaster and guest speaker on art, music and literature, and has appeared in conversation with figures such as Stephen Fry, Patricia Hodge, Krzysztof Penderecki, Edward Gardner and Petroc Trelawney. He was recently an invited lecturer at the English Speaking Union in New York.

He narrated his biography of Michael Tippett for BBC Radio 4's Book of the Week, his biography of Noel Coward (unabridged) for Audible and his book Jeoffry: The Poet's Cat for Spiracle Audio, joined by Stephen Fry.

A regular guest on the BBC and Times Radio, Oliver has appeared on programmes such as Front Row, Composer of the Week, Music Matters and In Tune. His work on the revival of Tippett's Symphony in B flat saw him interviewed for the 6 O'Clock News on Radio 4, and he is a talking head in BBC 2's documentary on Tippett's life.

As a speaker or interviewee he has appeared at dozens of leading arts festivals and venues, on topics ranging from Coward and Tippett to (at the National Galleries of Scotland) artist Barbara Hepworth and (at Southwark Cathedral) cats in the eighteenth century. In 2023, at the Duke of York's Theatre in London, he hosted a sold-out performance of Coward's revue London Calling, appearing with Damien Lewis and Indira Varma.