We can answer this question by considering the most significant event that occurs off-stage in the play, which is of course after Oedipus learns the truth about his identity and goes off-stage to gouge his own eyes out. There is particular significance in this event for a number of reasons that relate to the them. Firstly, it highlights the way in which Oedipus has been blind, willfully or otherwise, to the truth throughout the entire play. Secondly, it also indicates the kind of moral blindness that Oedipus has suffered from, as he has been unaware to truly see his own pride and how this is his tragic flaw. Thirdly, it also shows us how impossible and terrible his situation is as he literally cannot bring himself to look at the situation he now faces. Note the following speech that he says after re-entering the stage:
Dark, horror of darkness
my darkness, drowning, swirling around me
crashing wave upon wave--unspeakable, irresistible
headwind, fatal harbour!
Oedipus literally cannot bring himself to see either himself or the truth of his life, and thus this important action in gouging out his own eyes is immensely significant in order to support a number of key themes in the play. Off-stage action can therefore be analysed as strengthening and casting new light on the key themes of the play as this example shows.