Daughter of lawyer Ian Buttrose and his wife Elma, a violinist, Stroma was named after an island off the north coast of Scotland. Growing up on the coast at Brighton, she was educated at Hopetoun School 1936-40, Woodlands CEGGS 1941-47 and the University of Adelaide, where she graduated with BA (Hons) in Geography, 1956. She worked at different times as a common law clerk, a flower seller, secretary, grape picker, tutor, lecturer, and as an urban and regional planner from 1957-73. She was the first woman Master of Town Planning (University of Adelaide, 1972). In 1973 she was appointed Commissioner of the Planning Appeal Board/Tribunal, later to become the Environment, Resources and Development Court. She was the first woman to hold that position.
She retired in 1994. She has a ten acre property in the McLaren Vale area, which she is regenerating with native plants. Stroma began writing when she was about 15, and would read English and Australian poets aloud to herself, enjoying the rhythm and cadences and the words themselves. In 1953 she won the On Dit 21st birthday literary competition with three poems. She was a Member, later a Fellow, of the Fellowship of Australian Writers from 1960-72, holding various positions including Secretary in 1960 at the initial Adelaide Festival of Arts Writers Week, and a member of the Commonwealth Council of the FAW 1960-62. She has taken part in a number of Festival and other public poetry readings. Rigby commissioned her to write a children's reader, City Planning in Australia, which was published in 1975. She was a member of the Children's Book Council in the 1970s. She was a member of the Poets' Union of Australia and of South Australia and took part in Friendly Street poetry readings. She was a founding member of the Society of Women Writers (SA Branch) in 1976, holding the positions of Secretary, Vice President and later, Patron. Stroma is currently (1999) a Life Member of the Friends of the State Library of South Australia, a member of the Australian Society of Authors and of a private writing group, the Tatlers Club. She has served on numerous educational, arts, environmental and sporting organizations in various capacities. She has visited all the continents except Antarctica, yet, she says, Adelaide, where her close family also live, is always home.