Strickland was born in Birmingham, Alabama, the daughter of Theodosia and Lynn Strickland, who owned a tire shop. She had featured roles in 1970s films such as Bound for Glory, The Drowning Pool and Norma Rae. She also had a memorable appearance on the television series M*A*S*H as Captain Helen Whitfield, a nurse in an ongoing battle with alcoholism. Strickland played nurse practitioner Marilyn McGrath in the 1988 TV series HeartBeat. This was one of the earliest portrayals of a lesbian character on American network television. She guest starred in the Star Trek: Deep Space Nine episode "Paradise" as the character Alixus. She appeared in 11 episodes of Dr. Quinn, Medicine Woman from 1993-94 as the character Olive Davis. In 1994-1995, she appeared as Ms. Landis of Doubleday in the Seinfeld Season 6 episodes "The Chaperone" and "The Switch". She played Esther MacInerney in the 1995 blockbuster movie The American President. Strickland was a cast member in the brief run of the 2002 CBS television series First Monday, playing a Supreme Court justice.