Well seeing as one has an "r" on the end and one doesn't, it seems obvious, but....
Honour: like the word honor/honour, "AH-norr"
Ona: looks like OH-nah, could be like
Ana = AH-nah
Or if one is from Boston, he or she might say the word honor so it sounds like AH-nah, but I don't see that as the usual pronunciation.