She graduated from the Royal College of Art in 1955 and was art director of Jonathan Miller's production of "Alice in Wonderland" on television eleven years later. For the stage, she designed sets for The Importance of Being Earnest and Roy Doltrice's one-man show Brief Lives. Her opera designs included Otello, Swan Lake, The Nutcracker and La Boheme. She was known for her attention to detail.
Her entry into theatrical design was a curious one. While still in school, she heard Elgar's composition "Enigma Variations" and devised a way in which it could be made into a ballet. Sir Hugh Casson, a professor at the Royal College of Art, arranged for her to leave her drawings with Dame Ninette de Valois at the Royal Opera House. Choreographer Sir Frederick Ashton liked the work and gave Ms. Oman a call—twelve years later. Enigma Variations was finally staged in 1968. It was a success and ignited Ms. Oman's career.