Strudwick married Helen Wynn, (born Helen R. Sims), with whom he acted in stock theatre in Maine, on May 10, 1936, in New York City. They had a son in 1944. In 1949, he was married to Jean Mead, who had worked for the British Information Service. Strudwick was married to Mary Jeffrey from 1977 until his death. He died in New York City from cancer on January 15, 1983, at the age of 75.

He began his film career as the title character in the film Joaquin Murrieta (1938), credited as Sheppard Strudwick. He appeared as Yugoslav guerrilla leader Lt. Aleksa Petrovic, an aide to General Draza Mihailovich, in the 20th Century Fox war film Chetniks! The Fighting Guerrillas in 1943.

Strudwick made many appearances on television, including the role of Dr. Charles Morris in the 1958 Perry Mason episode, “The Case of the Fugitive Nurse.” He also appeared on The Twilight Zone, (in the episode “Nightmare as a Child”) and several roles on the soap operas As the World Turns (Dr. Fields), Another World (Jim Matthews), One Life to Live (Victor Lord) and Love of Life (Timothy McCauley). In 1981, he starred as the voice of Homer in the National Radio Theater’s Peabody Award-winning radio dramatization of the Odyssey.