Let's have some fun speculating different ways the Odium problem could be solved, shall we?
Dalinar magic-glues Honor back together. Fight. Win.
Dalinar gets the other surviving Shards to unite against Odium. Fight. Win.
Dalinar unites the Singers against Odium so the Fused no longer have willing bodies they can inhabit; Odium is left without pawns. Win.
Extensive use of Nightblood to deal perma-death to the Fused and other Voidbringers; no Odium-pawns. Win.
Drag out the war against the Voidbringers, repeatly killing the Fused until all of them lose their minds. Win.
Renarin goes around doing so much random stuff that Odium cannot predict the future anymore until CHECKMATE. Win.
Odium merges with Cultivation, then he cannot fixate on hatred&anger anymore because he progresses to the next stage of grief, bargaining. Win?
Cultivation wakes up from her long, long sleep and now she moves on to her next stage of grief, anger. Then she fights Odium and just wrecks him. Win.
Dalinar gets Odium to set a date for the duel of champions... a billion years away. Delaying the inevitable is win enough.
Adolin goes and talks to Odium and befriends him with his charming, sunshiny personality. Odium's like, "You just can't not like this guy!" and decides to not destroy humans. Win.
Hoid (or Susebron?) gathers up a ridiculous amount of Breath and Commands Odium to "stop being so mean and play nicer." Win?
Odium gets a big group hug and becomes less angry. That works on villains, right? No?
Something even bigger and scarier than Odium shows up, and humans and Odium have to unite and work together to survive. Win, but somehow worse?
Jasnah Soulcasts Odium into a statue of Moash. I know this wouldn't normally work, but there's so much Moash hatred in the fandom I think it could break the fourth wall.
Navani makes a hate fabrial and traps Odium in it. Win.
Shallan makes a big stick and speaks softly. Win.
Radiants take the Dawnshard, whatever that is, and shatters Odium with it. Win.
