It was uncanny returning to this choral ode after reading the whole play. You are right, I think, about its significance re: the rest of the play. The line that sticks out the most to me is 873: ὕβρις φυτεύει τύραννον (“Outrage produces kings”). Indeed, outrage (killing his father, marrying his mother) is what makes Oedipus a king. The chorus connects the general thoughts in the ode to Oedipus and his murdering Laius through imagery: ἔνθ᾽ οὐ ποδὶ χρησίμῳ (“where feet are useless,” l. 879) is an allusion to Oedipus’ name and condition and the mountain imagery of ll. 876-878 recalls Oedipus’ exposure on Mt. Cithaeron.
The ode presents an interesting religious problem: if the prophecies are not true, why serve the gods? If people stop believing in prophecies, then the whole edifice of Greek paganism is in danger of collapsing. Oedipus is faced with a horrible choice: accepting the truth of the prophecies and realizing what he has done OR denying the gods. Both of these are unimaginably terrible. The former is rejecting everything he knows about himself and living with the worst shame; the latter is rejecting everything he knows about the cosmos.
The choral ode does not say any of this explicitly, but it’s all there implicitly. Sophocles manages to put so much in such a small number of lines.