It looks like the Parshendi can bond Voidspren, which is what turns them into Voidbringers. Whether this can happen to humans is unknown though, but I would say its possible, because of this WoB:
Now, I know that Unmade and Voidspren are different, but I still think that if an Unmade could bond a human, the Voidspren could too.
I doubt Odium requires oaths for Voidbinding though. Since he most likely mind-controls the Voidbinders in some way, he wouldn't want to limit their power with a level-up system. In gaming terms, I think Honors forces (the KR) plays the game from the beginning, and level-up along the way, while Odiums forces (the Voidbinders) hack the game and starts on the highest level. So I doubt oaths exist at all with Voidbinders.