Thinking about this and this is what makes sense to me...
The Heralds, via their oathpact they are able to somehow bind and/or put to sleep voidspren. At the end of a desolation (or during it if they are killed) they would return to Braize (planet where Odium is trapped) and bring along the bound voidspren with them. A desolation would end, when either the remaining Herald's finished binding the voidspren on Roshar or they all died leaving some behind (but not enough to necessarily be a major impediment to humankind or due to the absence of Odium's influence after the desolation the voidspren would be very weak on Roshar). The reason for them having to go to Braize after binding as many voidspren as possible is that the voidspren on Braize are splinters of Odium and a sufficient number of them being on Braize ties Odium to Braize as opposed to Odium being able to travel to Roshar and attacking Cultivation and bringing massive destruction. The oathpact comes with multiple things. (1) allows the Herald to bind voidspren, (2) likely via the honorblade draw on the essence of Honor, and (3) in turn when they died or when the desolation was over they had to go to Braize and bring the bound voidspren with them there (in order to keep Odium there). Once the Heralds went to Braize, Odium would have to focus his attention on Braize, where he was, and the Heralds would feel the full direct fury of Odium until they broke, thereby returning to Roshar and freeing on Braize the voidspren they had bound. Once all 10 heralds would break Odium would from his limited vantage point on Braize turn his attention to Roshar and the voidspren would start making their way to Roshar thereby starting the next Desolation. If the Heralds would not act to bind voidspren within a limited amount of time, eventually it is possible enough voidspren would have been able to leave Braize and make it to Roshar enabling Odium to go to Roshar. The reason for 10 heralds, is to correspond to the 10 combinations of surges, which ensured the Heralds had the best ability to counter the voidbringers and bind as many of them as they could. In the last desolation, when 9 Heralds survived they had bound and put to sleep in a sense all or about all of the voidbringers. Taln who died, was back on Braize with the voidbringers he bound with him and that was enough to keep Odium's focus. As to why Taln was able to hold so long... One possibility is that by the other 9 heralds not bringing over their bound voidspren, Odium was weaker on Braize in the intervening period (due to having so many splinters asleep on Roshar). Alternatively as each Herald broke the voidspren he bound joined the torture, making it worse for the remaining. With the voidspren being asleep on Roshar, Taln, was not faced by as harsh a torture this time. - Regarding the oathpact, while Honor is dead and the Honorblades can no longer draw on his essence, they can still be used to bind voidspren, so the oathpact is still relevant.
At this juncture with the Herald's broken there is a real risk that the voidspren on Braize will make it over to Roshar, thereby freeing Odium. To prevent that someone will need to join the oathpact, or at least gain the ability to bind the voidspren and go back to Braize with them. This is what I think the end of book 5 might be. In other words rather this is preface to the true desolation where Odium finally breaks out of Braize, which will happen when whomever takes up the mantle of the Heralds, breaks. Further it would seem that other things will happen that will make Odium's escape inevitable. Beyond Odium being able to escape Braize, there is a bigger concern in the Cosmere that he will be able to eventually leave the Roshar system. I think this is why Nightblood is present... Nightblood seemingly completely destroys voidspren (or anything it touches) as such, it is destroying the splinters of Odium that bind Odium to Braize (and Roshar). If Nightblood is used excessively then Odium will not have any splinters holding him to the Roshar system. In this way, it makes a lot of sense that Naln does not care what Szeth is doing with the blade as he understands that Szeth is destroying Odium's prison(s). Viviena (Azure) is chasing after Nightblood to prevent the unintended consequence of using him form occurring.
With Honor dead, the strength of the binding of Voidspren weakened and whomever takes up the Herald's path, will only be a shadow of what they could do. Meaning that if someone goes to Braize with enough bound voidspren to prevent Odium from leaving, that binding will not hold strong regardless of whether the person can withstand Odium, leading to the eventual return of the desolation in Book 6. At that point with less voidspren around due to Szeth killing too many, Odium will easily make the move from Braize to Roshar, bringing the true desolation. Hoid who is out to stop Odium understands this and his goal his to shatter Odium. Likely he wants Cultivation to be a part of this which will result in both Odium and Cultivation being destroyed, thereby bringing some balance to Roshar (and preventing Odium from further threatening the Cosmere).
The Kinght's Radiant at the higher ideals are better able to move between realms and such, and therefore the presence of them somehow ties into being able to pull over voidspren from Braize quicker and hence the reason why the Skybreakers prior to swearing to the Voidbringers were looking out for anyone exhibiting such abilities.
I have some more on this but this outlines my major thoughts on this series and its place in the Cosmere.