After serving in the Austro-Hungarian Army during the First World War, Homolka attended the Imperial Academy of Music and the Performing Arts in Vienna, the city of his birth, and began his career on the Austrian stage.

Other stage plays in which Homolka performed during this period include: The first German performance of Eugene O'Neill's The Emperor Jones, 1924, Anna Christie, 1924, Boubouroche [fr], 1925, Juarez and Maximilian, 1925–1926, Her Young Boyfriend, 1925, The Jewish Widow, 1925, Stir, 1925, Mérimée and Courteline, 1926, Periphery, 1926, Neidhardt von Gneisenau, 1926, Dorothea Angermann, 1926–1927, Der Revisor, 1926, Androcles and the Lion, 1926, Bonaparte, 1927, The Ringer and The Squeaker by Edgar Wallace, both 1927, Underworld, 1930, Today's Sensation, 1931, The Last Equipage, 1931, The Waterloo Bridge, 1931, Faust, 1932, Karl and Anna, Doctor's Dilemma, Pygmalion, Juno and the Paycock, and many Shakespearean plays including: A Midsummer Night's Dream, 1925, Troilus and Cressida, 1927, Richard III, King Lear, and Macbeth.

After the Nazi party came to power in Germany, Homolka moved to Britain, where he starred in the films Rhodes of Africa, with Walter Huston (1936) and Everything Is Thunder, with Constance Bennett (1936).

Although he often played villains such as Communist spies and Soviet-bloc military officers or scientists, he was nominated for an Academy Award for Best Supporting Actor for his portrayal of the crusty, beloved uncle in I Remember Mama (1948).

He also acted with Ingrid Bergman in Rage in Heaven, with Marilyn Monroe in The Seven Year Itch, with Ronald Reagan in Prisoner of War and with Katharine Hepburn in The Madwoman of Chaillot.