Strangis is the niece of 1940s band leader, Comedian, TV star and RCA Victor recording Artist Spike Jones and the sister of notable Producer and Director Sam Strangis (Batman, The Brady Bunch, The Odd Couple, The Six Million Dollar Man). Judy was married in 1987.

Strangis' first appearance was in the 1957 movie Dragoon Wells Massacre, when she was seven years old. For the next 27 years, she was regularly cast in small and guest starring roles in television shows.

In 1969, Judy was cast as high school student Helen Loomis in the popular ABC show Room 222. She played this role for four years.

Strangis began doing voice-overs in Saturday morning cartoons in 1972 with william Hanna and Joseph Barbera's The Roman Holidays, as well as Wheelie and the Chopper Bunch in 1974 and continued performing cartoon voices-overs for the next 10 years for series including Goldie Gold and Action Jack, Saturday Supercade and MoonDreamers.

From 1974 to 1975, Strangis was a pitchwoman for Chrysler Corporation in the role of "Mean Mary Jean". Wearing a football jersey and short denim hot-pants, she promoted the Plymouth Duster, Plymouth Volare, and Plymouth Road Runner Models and often appeared at Chrysler promotions and auto shows around the country.

In 1976, Judy became a pitchwoman for Mattel's Barbie product line.

Other appearances include roles on The Spike Jones Show (Jones was her uncle), The Twilight Zone ("The Bard"), and Bewitched. She appeared twice as an extra on Batman; her brother, Sam Strangis, was a production manager on the show. In 1984 she guest starred in an episode of The A-Team "In Plane Sight" and appeared in the series CHiPs episode "Kidnapped".