The film is an appropriation rather than an adaptation because elements of the original play's plot and characters have been used in a different setting to create new meaning and explore the themes in a different way, in this case a parody of the original, rather than using the same story and characters and presenting it in a different frame, such as a novel instead of a play.
The title "Oedipus Wrecks" is a pun, in that it refers to both the Oedipal aspect of the protagonist (Woody Alan's character) wrecking his life and to the name shared by the play's title and it's tragic hero "Oedipus Rex." This humourus pun communicates to the responder that the movie is a comedy, and creates awareness that the film is an appropriation of the play.
As is so in the play, the inescapabilty of the character's fate becomes obvious to the responder, because, like Oedipus, Alan's character is a tragic figure who wants to do the right thing, but every attempt he makes to escape his fate draws him irreversibly closer to it.
Just as Oedipus causes his own downfall in genuinely trying to clear his name and investigates the facts too thoroughly, only to find out the horrible truth about his family, Alan's character goes to see a pyschic woman for help to escape his mother's burdensome presence, but she turns out to be just like the mother and eventually he ends up marrying her.
And like Oedipus, he does not realise what has really happened until after it is too late.
The movie uses fantasy, such as when the mother disappears in the middle of a magic show and reappears as a huge figure looking down on New York from the sky; stereotypes, such as the interfering Jewish mother; contrast, for example the difference between Alan's character's attitude and expression when his mother is present (dismay, panic) and absent (happiness, relaxation) from his life