We have a copy of your daughter Johannah's alphabet book, and she writes that omicron sounds like the o in smoke, while omega sounds like the o in arrow. To us, those are the same sound. In the book English from the Roots Up it says that omicron sounds like the o in obey, and omega sounds like the o in go. Again, these are the same sounds for us. But in Greek we must notice the difference.
Omega is the long of omicron, or omicron is the short of omega.
One of our friends had a year of it in college. We've tried 2 seminary texts, and have been thoroughly muddled and unhappy. We've now found EKS Publishing, in Berkeley, CA, which produces Hebrew materials for laypeople. I think I heard about it here in this discussion group. We're using the First Hebrew Primer, written for adults, and it's very easy to understand and use, and even fun.