Odium is a deity of some sorts, and probably is evil. His name is first spoken about in a vision Kaladin has. He later asks Syl if she had heard the name, and she hisses and flies off, the name obviously distressing her.
(Quote related to Odium beeing a Shard of Adonalsium and...)
"ODIUM COMES. MOST DANGEROUS OF ALL THE SIXTEEN."
A voice in Kaladin's dream, TWoK Chapter 46: Child of Tanavast.
(Quote related to The Thrill?)
Kaladin - “Why is there so much war? Must we always fight?”
Unknown Voice - "ODIUM REIGNS."
Kaladin's dream, TWoK Chapter 46: Child of Tanavast.
It is beleived that Odium is probaby a Shard of Adonalsium. His power is evidently hatred, and may have some relation to the Thrill that men feel at war.