Who earned both the Nobel Prize and Oscar award?

The only person to win both an Oscar and a Nobel prize was George Bernard Shaw.

He won his Nobel in 1925, for services to literature, including plays such as Arms and the Man (1894) and Saint Joan (1923), He won his Oscar, for best adapted screenplay, was for Pygmalion (1938), with Leslie Howard and Wendy Hiller, adapted from the 1913 play.