Oenslager was born in Harrisburg, Pennsylvania and became interested in design while studying in Europe. 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 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.
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."