The Oathpact is an oath held by the Heralds of The Almighty to protect the world in the times of the Desolations. During the Desolations, the voidspren came from Braize, also known as Damnation, to inhabit the listeners. This bond formed Fused, powerful parshmen with control over surges. Everytime a Fused was killed, the voidspren inhabiting it would simply be born again into a new host. This formed an impossible challenge for the humans, and so came the solution. The Oathpact. Five men and five women gave themselves up. With Honor's blessing, they traveled to Braize and sealed the spren of the enemy there. It prevented the voidspren of the enemy listeners from returning, and so ended the war. Or so Honor thought. While gods and spren cannot break oaths, men can and will. The voidspren captured the Heralds and tortured them. Eventually, one of the Heralds would break, starting a new Desolation. At the beginning, the Heralds were strong and hundreds of years passed between Desolations, but near the end, their souls wore thin. There were only 2 years between the last two Desolations. After the Aharietiam, the Heralds realized that after all that time, there was one Herald that had never broken their oath, and started a Desolation. Talenelat, the Bearer of Agonies. The other Heralds abandoned the Oathpact, leaving only Talenelat to uphold it by himself. For over four and a half millennia, Talenelat withstood the torture of the enemy, but he finally broke, joining the other nine who still live. This caused the True Desolation, currently occurring on Roshar.
The Heralds and the Shard Honor were the only two parties who were part of the Oathpact. Odium being bound to the Roshar System was not a direct result of the Oathpact but the Oathpact is part of it. 
After the Last Desolation, nine of the Heralds thought they abandoned the Oathpact, leaving only Talenel'Elin to uphold it. However, despite what they believe, all the Heralds are still bound to the Oathpact.
While at least some of the Oathpact still stands, it is unknown exactly how much remains.
- Prelude to the Stormlight Archive
- Words of Radiance signing Dayton
— Arcanum - 2014-03-19#
- Is the fact that Odium can't leave Roshar a direct result of the Oathpact, or something else?
— Arcanum - 2015-10-12#
- With the Heralds we know that there's only one left... one Herald that's still bound to the Oathpact--
— Arcanum - 2017-09-23#
- Is there any of the Oathpact still functioning because of Taln's continued participation?
— Theoryland - 2013-10-14#