To start things off, let's remember that all Cosmere events are background happenings throughout the many different novel. Meaning, they are not the focus of any of the novels. The main plot of each book and/or group/s of books each have their own respective focus.
Moving on, Odium's main focus is to destroy. This is important to remember for later...or throughout... your call. He wishes to be or become the most powerful being in the Cosmere.
Now, the chronological part:
Prior to Elantris: Oduim has already been there, destroyed that (Devotion and Dominion). Probably roughly 10 years prior to the novel. He has a way of using natural disasters to change things up a bit. (i.e. this is when the gods are fighting, this will come up again later.) (For those who do not know, I am speaking of the Chasm forming) So, logically unless another shard goes to Sel it is unnecessary for him to return.
The Emperor's Soul: Odium doesn't need to be there as he has already destroyed that. (the events of this novel take place on Sel). See previous note.
First Mistborn era Trilogy: It is unlikely that Odium is or has been present during these books, as he has probably already been trapped on Braize after or during his destruction of Honor on Roshar. (Also, we know that all the natural disasters on this planet where caused by the Lord Ruler) I believe it has been stated that Odium has been trapped on Braize for quite some time.(But not too long, you'll see later) Also, since there will be a third era Mistborn series, that seems like the most likely time for Odium to show up on Scadrial. (Or the inhabitants of Scadrial going to him...)
Moving on...
Warbreaker: Since this is after first era Mistborn, but prior to Stormlight Archive, Odium is probably on Braize, as previously stated, at this time. We do know that Endowment is there though, (on Nalthis) alive and kickin'.
Shadow for Silence in the Forests of Hell: I do not know what Shardworld this is on, nor do I know what aspect/s is/are there. But,... it is after first era Mistborn and before Stormlight Archive. So,... Odium is not there or influencing anything during this novel.
Stormlight Archive novels: Ok, so we know where Odium is (Braize). But, due to proximity he is influencing things on Roshar. Now, let's pause here to bring up some other things.
How trilogies usually work. First book, heroes win. Second book, villains win. Third book, heroes win and the story is over. Yay. Well, not in Brandon's grand scheme. Can't be. You cannot have Odium stuck on Braize for the entirety of The Stormlight Archive books. Also, he can't lose at the end of those novels. If this were true then why keep writing Cosmere books. You can't just bring in a new villain partway through and go "Oh, hey, yeah, there's this new guy and he is worse than the last. Bwahahahaha." ... So, logically Odium will either succeed at getting off Braize and since he was in the neighborhood, kill Cultivation on the way. I mean, he was already in town, might as well stop on by and kill a shardbearer. When should this happen you might ask? At the end of book five. Here's why, there is supposed to be a fifteen year gap from book five to book six due to some big event... Like the end of the Desolations...(natural disasters, remember?) because Odium has left the building. But, the books continue, because as I said, the Cosmere events are not the MAIN events in the novels. They are the background fluff. (Albeit they are the most interesting fluff I've ever seen. And I've seen cotton candy.)
Onward Fearless (and probably bored with me) Adventurers...
Alloy of Law: Due to this being a transition novel from one Mistborn era to another, what better time to screw with readers. We will leave it at that. All speculation is automatically allowed. Any Shardbearer (excluding dead ones...) can do whatever they want!
Shadows of Self, or Second Mistborn era: This takes place 342 years after the events of The Hero of Ages. Which means all the books between first and second Mistborn eras happens in under 342 years. Geez, Odium had little time to sit around on Braize. But wait, if Elantris is only hundreds of years (not thousands) of years prior Mistborn, and Stormlight is before Second era Mistborn, then... Oduim could not have been trapped on Braize for too long (relatively speaking for a "god"). Now, we have not seen any natural disasters in this series yet. (the flooding was caused by Bleeder, therefore not natural disaster). We can likely conclude that Autonomy showed up, which would explain Bleeder acting all revolutionary. Rise up against Harmony she says. Foil hats everyone. And, this could explain the rusting on the spike at the end. It is an direct effect to the metal not allowing Harmony (Sazed) to control people. Good for Autonomy (Bavadin), not sure how this is useful to Odium... Except that if Autonomy were attempting to break apart Harmony (due to the speculation that he may have a desire to make sure the shards were autonomous) it would then give Odium a leg up on Sazed because he would no longer have two shards. So, Autonomy isn't the new worse villain, he is the transition villain in the transition era. Oh, hmm that makes sense if we are leading to a final Mistborn era that should and most likely involve the end of Brandon's Cosmeric Conflict with Odium.
Well, to sum things up. I believe that Odium causes natural disasters. These disaster are either the fight between gods or the aftermath of the smashing a shard. Since there hasn't been any on Scadrial, I believe Autonomy to be there, not Odium. I also think that at the end of the Desolations (in the Stormlight novels), that Odium has left the Greater Roshar system and is moving on. I also believe that we will not see Odium on Scadrial until the third Mistborn era (which I do believe Brandon has said would be the end of his Cosmere inspire books).
That is interesting...
Your thoughts!