In 1910 she joined the St John Ambulance Brigade and rapidly rose through the ranks. On the outbreak of the First World War she was put in charge of the Naval and Military Volunteer Aid Detachment (VAD) Department, which administered the combined nursing staff of St John Ambulance and the British Red Cross Society. She held the post throughout the war, but resigned in 1922 in opposition to plans to disband the VADs. She later joined the British Red Cross Society as head of its VAD department. During the Second World War she was a member of the Society's War Organisation Executive Committee and several other committees. After the war she became the Society's Director of Education, retiring in 1956. She then became the BRCS's archivist and published its definitive history, The British Red Cross in Action, in 1966.
In recognition of her work in the First World War, Oliver was awarded the Royal Red Cross (RRC) in 1916, appointed Commander of the Order of the British Empire (CBE) in 1919, and raised to Dame Commander (DBE) in the 1920 civilian war honours. In recognition of her work in the Second World War she was promoted to Dame Grand Cross (GBE) in 1948.