The Overlords are essentially the oldest, most evil creatures in existence. There very existence would corrupt the land around them for miles were it not for the bindings that keep them from emerging into the world (the binding are not to be confused with the Silver Flame, which is related but something different). And in order to imprison these creatures, it required nearly every couatl in existence to sacrifice their lives to power this magic. In Eberron, the couatl is the closest thing they have to divine beings that actually at some point walked the world and interacted with mortals. They are the divine good, and the overlords are the divine evil. Overlords are more of a universal threat.
The Quori, through their Inspired vessels, have created a nation akin to North Korea. Their goals are two fold. First is to prevent the Turning of the Age. Quori are reflections of Dal Quor, the realm of Dreams. Currently, they are in the third age, il-Lashtavar or the Darkness that Dreams. When Dal Quor inevitably shifts once more, all Quori on Dal Quor will be changed to reflect the new age, whatever that may be. While the individual essence of each Quori will remain, their personality will change and their memories will be erased. There is some thought that the Quori of the second age attempted their incursion into Eberron (resulting in the Giant-Quori War) as a means of preventing this fate. The current leaders of the Quori also believe that any Quori that do not align with the purpose and goals of the masses may trigger the turning of the age. That is why the Kalashtar exist. These were separatists that believed in something different. The Quori leaders sought to kill these separatist Quori. But since Quori cannot truly die, killing them on Dal Quor would return their essence to the Dreaming Dark to be reformed into something that more resembles it. Thus they found a way to escape Dal Quor and make it difficult to kill them. The second goal of the Quori would be to infiltrate Khorvaire and remake it in the image of Reidra, giving them power over mortals and thus greater control over the mortal dreams that shape Dal Quor.
The daelkyr around probably the least understood of the big bads. While the daelkyr led the invasion from Xoriat, no one knows why. They did not have any clear reason. While they are the most powerful creatures to emerge from Xoriat, they are not the most powerful creatures of Xoriat. The daelkyr may have been explorers attempting to terraform eberron to their own purpose, creatures believing in their own superiority and attempting to rehabilitate the "savages" of eberron in the only way they know how, or they may be some kind of artists and they saw eberron as a new and exciting canvas. They may not see the creatures of eberron as alive by their own definition, or if they do may see Eberron's life as having no more value to them as ants have value to us.
These 3 bad guys represent different opportunities for themes. The Overlords are classic good versus evil. The Quori provide an opportunity the explore the gray areas the exist by interactions with the culture and people's of Riedra, and an enemy that is attempting to better control their own fate and destiny. And the Daelkyr represent the truly alien. Creatures that cannot be reasoned with or understood, and have no interest in reasoning with or understanding those they harm.
Also, go read Keith Baker's blog at Keith-baker.com. It is a wealth of information on how to approach and run these guys.
