Strasser's birth name is Robin Victory in Europe Strasser, as she was born the day Germany surrendered in World War II. She was born in the New York City borough of the Bronx and raised in Manhattan by Martin and Anne Strasser. After graduating from the High School of Performing Arts, on full scholarship, she attended the Yale University School of Drama. She began acting in the early 1960s. Strasser sharpened her acting abilities in theatre, acting on Broadway, where she appeared in The Shadow Box and Chapter Two. Early in her stage career she met her first husband, Laurence Luckinbill; they were married in 1965 and divorced in 1976. They have two sons, Nicholas (born 1971) and Ben (born 1975). Strasser was also married to Richard Hogan from August 27, 1983, until 1985.