Trevor was the eldest of three sons born to Arthur and Ethel Oldham, he was educated at Melbourne Church of England Grammar School and the University of Melbourne. Oldham graduated in law at Melbourne University in 1921 and practised as a solicitor until the weight of parliamentary duties limited his time.
He had enlisted in the Australian Imperial Force on 7 November 1918, four days before the Armistice. He was a past president of the Royal Victoria Eye and Ear Hospital and a former deputy chancellor of Melbourne University. Oldham was a former director of Henry Berry & Company, Hoadley Chocolates Limited, Ruskins Motor Bodys Limited, and Ensign Dry Cleaners Limited.
Oldham served as Attorney General in Thomas Hollway"s first government in 1947, and he also served as Deputy Premier of Victoria for 8 months before the Liberals lost office to a Country Party and Australian Labor Party alliance in 1950.
In 1951 Les Norman replaced Hollway as Liberal leader after the party grew lukewarm on Hollway"s plan of reforming Victoria"s malapportioned electoral boundaries.
With their leader having been defeated the Liberal Party elected Oldham as leader and Henry Bolte as deputy leader. The BOAC Comet crashed near the village of Jangipara a few minutes after leaving Calcutta.
At the time a 60 mph dust storm and torrential rain were sweeping the area. Indian authorities arranged a communal burial of all victims of the Comet air crash in Calcutta.
A memorial service was held at Melbourne"s Street Paul"s Cathedral on 6 May 1953.
Oldham entered parliament in 1933 as a member of the United Australia Party, he won the seat of Booroondara and held it until the seat was divided in 1945.
