Personally, I think Hoid is trying to get revenge because of a personal vendetta. At every possible moment in The Stormlight Archive, Hoid is going against Odium by helping Shallan, Dalinar, and even Kaladin to an extent. He helps Jasnah when she gets back from her visit to Shadesmar, and it is possible that he helped Lift, seeing as how she remembers a crazy old man who jumps into a greatshells mouth - Hoid fits the profile. Also
It makes sense that Odium would've killed someone close to Hoid. After all, he's sort of almost like maybe half a Shard.