Can you help me understand what Deus ex Machina is and give me some examples of it from the Odyssey?
Deus ex machina is when a force comes in to 'save the day' (for lack of a better phrase) unexpectedly, and I'd say any example of this from the Odyssey is interference from the gods.
To better understand Deus Ex Machina, perhaps this definition from urban dictionary can help you: "Dates from ancient Greek times, where "deus ex machina" ("god from the machine") in a play referred to the act of lowering a god on stage using a cable device (therefore, a god from a machine) to decide in a dilemma and give fate a nudge, so to say."
The first thing that comes to mind in the Odyssey is the fact that many gods help to nudge Odysseus' story along -- like Poseidon's anger & shipwrecking Odysseus, and stuff like that. One example you might use is Athena's constant guidance over Telemachus.