Olah was born on 13 March 1910 in Vienna. He attended school in Budapest for three years. Olah returned to his native Vienna from Budapest where he learned to build pianos. He also began developing ties with Austrian trade unions and the Social Democratic Party of Austria during this period of his life.
Olah found himself in trouble with the police during the 1930s. In 1938, Austria lost its independence and was annexed by Nazi Germany during the Anschluss, which brought the rule of Adolf Hitler and the Nazis. Olah was arrested by the Nazis following the Anschluss and deported on the very first train to transport Austrian prisoners to the Dachau concentration camp in 1938. He was transferred as a prisoner to several German concentration camps throughout World War II. Olah was finally freed shortly before the end of World War II.
Olah was elected as a member of the Austrian Parliament in 1948. He served as second president (Zweite Präsident) of its lower house, the National Council, from 1959 until 1961. He next served as the Austrian Interior Minister from 1963 until 1964.
He founded the now defunct Democratic Progressive Party (Demokratische Fortschrittliche Partei) in 1965. The party garnered more than 3% of the vote in the 1966 Austrian legislative election, but failed to win any seats in Parliament. In 1969, the Democratic Progressive Party won three seats on the Vienna city council.