With a Moses AND a Dempsey, I would say that your line connects to mine. The proper spelling is actually Odum, but it has been mispelled in various documents and by clerks using phonetic spellings, I'm sure (supposition on my part).
I don't seem to find anything that connects you directly to my lines that I have documented, but I'm sure that you do. My eldest Odum is Moses Odum and wife, Rachel. I descend through son Moses, who married Elizabeth Christian. From them, I descend through their son Wiley Odum who married Sarah Kitching. Their son, Dempsey Odum, was a member of the house of Representatives for the state of IL, and my 3rd Great-grandfather. He married Sarah Jordan. From them, I descend through daughter Martha Odum and I lose the Odum surname from there.
You can view my Odums on my web site at: http://freepages.genealogy.rootsweb.com/~thall
The names that are most often used in this family are: Moses, Dempsey, and Wiley. They moved from NC (1700's) to TN then up into IL.
Write to me if you discover that we do connect!