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. In 1973, she appeared as Sister Ann, in the season four episode, "Almost a Nun's Story", on The Mary Tyler Moore Show.

Strickland had a memorable appearance on the television series M*A*S*H as Captain Helen Whitfield, a nurse in an ongoing battle with alcoholism. She appeared in the pilot episode of the television series Night Court as the public defender. She also guest starred in the Cagney & Lacey episode "Fathers and Daughters" (4.5). Strickland played a struggling rancher's daughter in the 1987 Highway to Heaven episode "A Dream of Wild Horses", alongside legendary actor Richard Farnsworth. She 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.

Strickland appeared in 11 episodes of Dr. Quinn, Medicine Woman from 1993–94 as the character Olive Davis. She guest starred in the Star Trek: Deep Space Nine episode "Paradise", as the character Alixus. In 1994-95, she appeared as Mrs. Landis of Doubleday in the Seinfeld season 6 episodes, "The Chaperone" and "The Switch". She appeared on the U.S. Navy series JAG first season episode "War Crimes". She played Ambassador Bartlett, the U.S. ambassador to Peru. Strickland also played Esther MacInerney, the wife of A.J. MacInerney (Martin Sheen), Chief of Staff for President Andrew Shepherd (Michael Douglas), in the 1995 movie The American President. She played Dr. Rene Spielman on ER season 6, episode 6, "The Peace of Wild Things".

Strickland was a cast member in the brief run of the 2002 CBS television series First Monday, playing a Supreme Court justice.