We know from the second letter in Words of Radiance that Odium is trapped in the system he currently inhabits (Roshar). My theory is that Odium has invested in Roshar, specifically in the stone surface itself.
The Shin stone shamans believe the stones are holy and should not be walked on. I think this is a perversion of an ancient truth: you don't walk on stone when the spren of your enemy can turn the stone underneath you into a giant rock monster (ThunderClast). Szeth notes that the stone shamans say it is OK to walk on the stone at Urithiru in the I-10 WoR interlude. Jasnah states that some stories claim Urithiru is protected from Voidbringers. My conclusion is that it is OK to walk on Urithiru stone because Voidspren can't bond with it and turn it into monsters.
Chapter 6, Jasnah:
I-10, Szeth (in Urithiru):
Another reason I think Odium is invested in the stone is that certain spren associated with negative emotions like Angerspren, Painspren and Anticipationspren (associated with battle) all have red or orange colors and come out of the ground and stay connected to the ground. Unlike more positive spren like joy or glory spren that float around in the air (like honorspren). All these spren associated with pain, anger and battle are sprouting from Odium's investiture in the stone.
From Coppermind Spren Entry:
“ Vamah was watching them stand there, and his expression was as thunderous as a highstorm, angerspren boiling up from the ground around him like small pools of bubbling blood.”
— The Way of Kings: Chapter Fifteen[35]
“ Painspren swarmed the ground, like small orange hands or bits of sinew, reaching up from the ground amid the blood of the fallen.”
— The Way of Kings: Chapter Forty-Seven[59]
Anticipationspren:
“ A few anticipationspren—like red streamers, growing from the ground and whipping in the wind—began to sprout from the rock and wave among the soldiers.”
— The Way of Kings: Chapter Six[14]
A common type of spren that appear around people looking forward to something. They appear as red streamers that grow out from the ground and blow in the wind. They often appear around soldiers directly before a battle.[14]
Finally, when Tanavast appears to Dalinar in chapter 75 of WoK, Tanavast shows a dark stormwall approach and destroy all of the ground around Dalinar and Tanavast. Tanavast says "this is what he wants". Odium needs to free up his investiture in the stone surface of Roshar in order to leave the system fully powered up.
http://www.tor.com/2014/05/15/the-way-of-kings-reread-chapters-74-and-75/