It is worth noting that the style of Oedipus Rex is partly a product of the translator as well as Sophocles himself. While Fagles (in the edition cited in this guide) is attempting to capture the meaning of Sophocles's writing as best as possible, there is always something lost in translation. Nevertheless, there are many elements of Sophocles's style that can be gleaned from the English translation.
Overall, Sophocles uses a formal writing style rich with figurative language. Given that the characters are frequently speaking to their king, Oedipus, Sophocles's formal and elevated style is highly appropriate. Sophocles's style was notably different from his contemporaries: he is credited with adding a third character to the drama, reducing the role of the chorus, and focusing more on character development. While it is hard to understand the full effect of these stylistic differences without reading earlier Greek plays, they are nevertheless evident throughout.
At the same time, like much of the Greek writing that has survived into modernity, Sophocles makes frequent use of figurative language. Sophocles's writing relies heavily on dramatic irony, or the ironic disconnect between the character's knowledge and the audience's (or reader's) knowledge. Greek spectators would have already known the story of Oedipus, just as many modern readers approach the story with some understanding of Oedipus and his failings. Regardless, Sophocles foreshadows the play's conclusion frequently throughout the play, developing an awareness in the audience and the reader that Oedipus lacks. Sophocles's specific diction and syntax foster a sense of dramatic irony as the play develops, creating a mounting feeling of dread in the reader and audience.