What would you say inspired the writing of the Aeneid and the Odyssey. Something that is relevant to both poems.

Answer 1

Iliad and Odyssey were composed and recited long before they were ever written down. They arose in the areas around ancient Greece and were told and retold for several hundred years before they were written down.
http://en.wikipedia.org/wiki/Iliad
There are still disagreements about who actually composed these or even it they were composed by a single person.

Aeneid, however, was written purposefully by the Roman poet Vergil (sometimes spelled Virgil). His inspiration was a character already known in the Roman world from Greek mythology (Aeneus), but Vergil wrote this poem to give people a strong connection between the young Roman culture and the ancient Greeks.
http://en.wikipedia.org/wiki/Aeneid

Answer 2

I always told my classes that writers motive has always been from earliest times - Does man or god control man's fate? Look for this theme in both of these stories. You might also check these sites.

http://www.sparknotes.com/lit/aeneid/themes.html

http://www.sparknotes.com/lit/odyssey/themes.html