I found Stormfathers reaction to be curious. He's not sure, yet accepts the words. Feels like it's part of something that honor was part of. You see the trees but not the forest thingy. When Stormfather says this hasn't happened before, Dalinar replies
1) This shows Unity is different from Honor due to Dalinar will.
2) If it was so different and new (Dalinar specific) then Odium should not have recognized it, but he does.....
3) it's curious that Dalinar differentiates between Honors remanents and Stormfather soul. Means he's more than just a shadow of honor as described elsewhere. Stormfather may be Honor mixed with a bit of Cultivation.
A even more radical theory...
The only explanation when all above could be true is when we assume Unity is Adonalsium. It's different because Dalinar has taken a step above Honor. This is possible because Honor and Cultivation has lot more overlaps and intrinsically mixed than we know for now. Perhaps Dalinar absorbed some if Cultivation influence (though she's still alive) through Honor. Odium recognizes Unity because it's still an aspect of Adonalsium than Honor.
Is Unity referring to Adonalsium? When Odium says "We killed you" he's probably referring to the splintering and killing of Adonalsium and not Honor. (Also Harmony is a subset of Unity. Without Harmony there cannot be Unity )
Perhaps the end result of the series would be to reunite Adonalsium and complete the circle. Possibly at end of Dragonsteel. Dalinar becomes the aspect of Adonalsium and unites all shards back.
I'll get back to my drink.