The story
From groady, apparently a clipping of grotesque + -y (intervocalic /t/ and /d/ are similar in American English). Compare British grotty, of the same origin, and gro. Popularized by Moon Unit Zappa in song "Valley Girl" (1982) in phrase "grody to the max", as archetypal Southern California Valleyspeak; song also popularized "gag me with a spoon".
Etymology from Wiktionary, CC BY-SA 4.0.