How does the motif of Divine Intervention influence the plot in this book?

The gods exercise absolute power over mortal actions in The Odyssey. To curry the gods' favor, mortals are constantly making sacrifices to them. Conversely, offending the gods creates immense problems, as demonstrated by the oxen of Helios episode and Poseidon's grudge against Odysseus for blinding his son Polyphemos.

Athena is the most visible god in the poem; only under her aegis can Odysseus survive his dangerous adventures, and she lobbies Zeus for his freedom and safety at other points. Her favoritism for him seems justified as a reward for his sacrifices and nobility of character; her distaste for the suitors is similarly understandable.

The power of the gods, who usually care more about their internal disputes than about mortal behavior, is cemented at the end of the poem as Zeus orders a cease-fire between Odysseus and the suitors. Ultimately, the gods decide what happens in the mortal world; lack of free will receives more depth in The Iliad, but is a prominent theme in nearly any ancient Greek text, particularly ones that concern themselves with the omnipotent gods.