I agree that you are all on to something. Are we sure that "Odium" is the shard's intent? From OB, chpt 56:
"I'm the other one, Dalinar. They call me Odium." (emphasis mine)
Odium is what he is called, but what is he really? Out of curiousity, I looked up odium on several dictionaries. The original latin word meant hatred, but an alternative meaning in modern english is hated. Maybe Odium is just a label assigned by those who knew Rayse, combined with the shards actual intent.
I agree that Hunger or Excess seems more accurate. Or maybe Intemperance.