In modern Greek there's no real difference. The sound is "o" as in "not" (お).
In the past they are supposed to have had a different pronunciation. In some areas of Greece they have, somehow, kept those differences until today..
Ο ο: όμικρον (omikron) the little o → the sound would last for a short time.
Ω ω: ωμέγα (omega) the great o → the sound would last for longer.
But you won't notice any diffence most, if not all, of the times. The sound is that of the SHORT "o".
Today where you use each one is mostly a matter of spelling. There are some rules, but not for all occasions. Mostly for endings of words.
When you don't know what a word means, how it's written can often indicate or help guessing the meaning. At least give you a feeling about what that word means. Because words with the same root will be written similarly..
The same goes for ι, η, υ, οι and ει. All share the sound "i" as in "sit" （い）.
And the same goes for ε and αι as well. They share the sound "e" as in "pen" （え）.
I hope this helps!!