Oenslager was born in Harrisburg, Pennsylvania and attended Harvard University, graduating in 1923. He became interested in design while studying in Europe and his first work as designer was for the ballet "Sooner or Later" in 1925. He had started as an actor in the 1920s at the Greenwich Village Theatre and the Harrisburg Playhouse.
He designed sets and often lighting for more than 140 Broadway productions between 1925 and 1975. In 1959 he was awarded the Tony Award for Best Scenic Design for his work on Leonard Spigelgass's play A Majority of One. He had received a Tony nomination two years earlier for his work on the play Major Barbara.
He taught scenic design at the Yale School of Drama for many years  and the institution continues to award an annual scholarship for stage design in his name. Among his notable pupils was John Lee Beatty.
Oenslager's papers are held by the New York Public Library for the Performing Arts, although a number of his scenic design sketches are part of the permanent collection at the Museum of the City of New York. The Museum had an exhibition of his designs in 2008.
He brought "a new emphasis on symbolism over realism to American theater design."
- Donald Oenslager papers and designs, 1922-1982 held by the Billy Rose Theatre Division, New York Public Library for the Performing Arts, retrieved March 5, 2010
- Setting the Stage: Scenic Designs by Donald Oenslager Archived July 6, 2010, at the Wayback Machine. Museum of the City of New York, retrieved March 5, 2010