Born in New York City and raised in the upscale suburb of Croton-on-the-Hudson, Strauss was focused on acting from an early age and appeared in productions of "As You Like It" and "Romeo and Juliet" with the Croton Shakespeare Festival while still a teenager. He also worked in summer stock while attending Northwestern University's famed acting program. Upon graduation, Strauss set out for Los Angeles where a screen test earned him the supporting role of Michael Douglas' black sheep brother in "Hail, Hero!" (1969). After appearing at the Mark Taper Forum in Los Angeles in "The Dance Next Door", Strauss won his first screen lead in "Soldier Blue" (1970), as the Wild West soldier sent to bring Candace Bergen back to civilization but who ends up understanding her devotion to the rights of Native Americans. Strauss' subsequent film appearances have been sporadic, including co-starring roles in "The Trial of the Catonsville 9" (1972), "The Last Tycoon" (1977) and "Nick of Time" (1995). The actor found his niche on the small screen.

In 1973, Strauss made his TV-movie debut in "A Man Without a Country" (ABC) and in the two-part "Attack on Terror: The FBI Versus the Ku Klux Klan" (CBS, 1975), he played a character loosely based on Michael Schwermer, one of three Civil Rights workers who were killed in Mississippi in the 1960s. After his success with "Rich Man", Strauss went on to appear in several above average telefilms including "Joe: The Forgotten Kennedy" (ABC, 1977) and "The Jericho Mile" (ABC, 1979), written and directed by Michael Mann. For the latter, Strauss won a 1979 Emmy as a Folsom Prison inmate who becomes a long-distance runner. In 1981, he moved behind the camera, serving as executive producer (as well as star) of "A Whale for the Killing" (ABC), about a bay community which attempts to save a whale from death when it becomes stranded in its harbor. That same year, Strauss starred as the leader of the Judeans resisting Roman domination in the ABC miniseries "Masada". Strauss was a steelworker in "Heart of Steel" (ABC, 1983), which he also executive produced. He played Dick Diver in the miniseries adaptation of F. Scott Fitzgerald's "Tender Is the Night" (Showtime, 1985), the FBI director in "Under Siege" (NBC, 1986), and a martial arts expert trained to be an assassin in "Brotherhood of the Rose" (NBC, 1989). Strauss continued as one of the few men whose name carried a TV-movie in the 90s. He was a cop obsessed with finding a convict in "Fugitive Among Us" (CBS, 1992) and the following year took a role with far less heroic bravado in "Men Don't Tell" (CBS), as a husband physically abused by his wife. Strauss was the father in the 1994 CBS remake of Marjorie Kinnan Rawling's "The Yearling", a millionaire marrying his mistress in "Texas Justice" (ABC, 1995) and a politician coping with defeat in "In the Lake of the Woods" (Fox, 1996). Strauss took the weekly series plunge for the first time playing a police psychiatrist in the drama series "Moloney" (CBS, 1996-97).