Oedipus rex was written towards the beginning of Stravinsky's neoclassical period. He had considered setting the work in Ancient Greek, but decided ultimately on Latin: in his words "a medium not dead but turned to stone."
Many insights to this opera are found in Leonard Bernstein's analysis of it in his sixth and last Norton lecture from 1973. Bernstein stated that Oedipus Rex is the most "awesome product" of Stravinsky's neoclassical period. Much of the music borrows techniques from past classical styles and from popular styles of the day as well. However, Stravinsky purposely mismatches the text subjects (in Latin) with its corresponding musical accompaniment.
Bernstein even goes so far as to link the opening four-note motif sung by the chorus to a specific sung quote in Verdi's Aida. The idea parallel of "power and pity" reigns in both operas even though the specific subject matters are quite different.