[7] Stoddard's first professional stage appearance was in San Francisco in 1934[8] as a walk-on/under-study in a production of Merrily We Roll Along, before she succeeded to the ingenue's leading role for opening night in Los Angeles.

[10] She subsequently starred in A Woman's a Fool – To Be Clever, I Know What I Like, and Kindred (all 1939), Susannah and the Elders (1940), Mr. and Mrs. North (1941), The Rivals (1942), The Moon Vine and Blithe Spirit (1943), Dream Girl (1945), and The Voice of the Turtle (1947).

She starred in Joan of Lorraine, The Trial of Mary Dugan, and The Voice of the Turtle (1947), Rip Van Winkle (1947–48), Goodbye, My Fancy, and Her Cardboard Lover (1949), Affairs of State (1950), Springtime for Henry (1951), Twentieth Century, Glad Tidings, and Biography (1952), ten summer stock productions at Denver's Elitch Gardens Theatre, and The Frogs of Spring, a revival which she co-produced with husband Harold Bromley on Broadway (1953).

Stoddard and Jack Kirkland were original share-holders in the creation of the Bucks County Playhouse in 1938; she appeared there in a total of sixteen productions from 1939 to 1958, including The Philadelphia Story, Golden Boy, The Play's the Thing, Petticoat Fever, Our Betters, Skylark, and Mr. and Mrs.

as Come Play with Me starring Tom Poston and Liliane Montevecchi in 1960, and with Mark Wright and Leonard S. Field premiered Harold Pinter on Broadway in 1967 with The Birthday Party.

She later offered Off-Broadway productions of Coward's Private Lives (1968), co-producing with Mark Wright and Duane Wilder; Lanford Wilson's Lemon Sky (1970) and The Gingham Dog (1971), and The Last Sweet Days of Isaac, a musical by Gretchen Cryer and Nancy Ford (1970) which won three Obie awards.

With Neal Du Brock she produced The Survival of St. Joan (1971); and, with Arnold H. Levy, Lady Audley's Secret (1972) and Love, based on the play by Murray Schisgal, starring Nathan Lane (1984 Outer Critics Circle Award).

Pursuing her interest in young playwrights, she produced off-Broadway productions of Glass House (1981), Casey Kurtii's Catholic School Girls (1982 Drama Desk Award), Sweet Prince (1982), Marvelous Gray (1982), and John Olive's Clara's Play (1983).

Her dramatic adaptations of Thurber material include Life on a Limb, and Men, Women, and Less Alarming Creatures, produced with The Last Flower on Boston WGBH-TV public television in 1965.

She also directed the national touring production of Lunatics and Lovers, and she wrote original scripts entitled Abandoned Child and Bird on the Wing, and co-wrote Dahling – A Tallulah Bankhead Musical with composer-lyricist Jack Lawrence.

Stoddard also served as understudy to such acclaimed actresses as Bea Lillie, Greer Garson, Betty Field, Rosalind Russell, Uta Hagen, Mercedes McCambridge, and Jessica Tandy, in various stage productions.

[9] Stoddard succeeded Elaine Stritch as the matinee Martha for in the original 1962 Broadway production of Who's Afraid of Virginia Woolf?,[9] playing the part each Wednesday and Saturday afternoon, and standing by in her dressing room each evening until the curtain rose for the second act with Uta Hagen safely in command on stage.