I've just had the listening exercise in "strengthen skills" with omega and had the letter ω marked as wrong.(contrary to what "jaye16" says). Whatever the value of these alphabet exercises in the early stages of the course, surely they should not be repeated within the strengthen skills section when the student has already completed the course and is simply trying to reinforce vocabulary.
They sound completely different in modern Greek: η makes the /i/ sound as in "seen", ε makes the /e/ sound more or less as in "hen".
It's harder to know when to use η, ι, υ, οι, ει (which all make the same sound) or ε, αι or ω, ο.
When they're part of the word root, you just have to learn it -- as with English "ee, ea" for example.