Green’s Dictionary of Slang

(US campus) a condition of having one’s underwear caught between the buttocks; thus have a murphy.

1989		P. Munro Sl. U.
1991		J. Algeo Fifty Years Among the New Words (1993) 241: 1990 Fall. Wedgy appears to be a term for a high-school prank [...] Connie Eble reports the synonyms melvin and murphy.