Hang on.
What are the Ten Deaths?
I assumed, when I first read the quote, that they were just a type of Voidbringer... or weren't there 10 Desolations? Maybe its just another name for those. I'm not sure, especially now that I've finished the book and I'm looking back at the quote.
On topic, I agree that the Thrill seems like an almost inhumane bloodlust. Its quite plausible that Odium influences it in someway, although I don't think Brandon uses a direct connection like the one that Ruin has with Hermalurgic spikes. I toyed with the idea that shardplate gave a person a more powerful version of the Thrill, but I discarded the idea. The more I think about it though, Kaladin is an amazing fighter, perhaps parallel in abilities to Dalinar, but he does not experience the Thrill in the same way that Dalinar does. The Thrill almost controls Dalinar in a battle, while Kaladin is more in control of himself, relying on the Stormlight to guide him through the battle. The Thrill COULD be an influence from Odium, while Stormlight is perhaps the leftovers of the Almighty (or another Shardholder's) influence on Roshar. We already know that, even after a shardholder has "died", or whatever happens to them, they can still influence the world (see Mistborn). In Mistborn, Leras' connection is Allomancy, and it still works even when he is gone.
As I typed that paragraph, I changed my views a lot, and made a lot more connections than I originally was thinking. Anyone have any other ideas about the Thrill?