Odio has incarnations. They’re essentially versions or parts of himself that pop up throughout time and space to do evil and make a point about the vices of humanity and what Odio believes to be right, whether it be through their own actions (Odi Wang Lee), what humans do for them (Odeo) or what was done to them (O. Dio and arguably OD-10). But there’s a bit more to them than that.
See, for one, Odio’s incarnations have always existed even before Oersted became the Demon King, because he always was the Demon King (see: a meta I really need to write up about temporal stuff and how that relates to Oersted and his weird status of both being Odio and also not being Odio because hoo boy). Two, his incarnations aren’t necessarily Odio reincarnating himself every so often to torment humans. They’re projections. Aspects of himself he cast out into the universe through the statues in the Demon King’s castle. They’re both their own beings but also... not. The best way to describe Odio’s incarnations would be automatons that Odio watches over. He sees what they see and knows what they know, but for the most part they act on their own, though those actions arguably are always inherently linked to Odio’s own desires since, well, they’re him in a roundabout way.
But I mention in my verses page that Odio can be more present in his incarnations. And he does this by possessing them essentially. In the final chapter, if you select Oersted as your player character, you get to play as the incarnations in a boss rush. The curb-stomp battles that ensue are arguably the result of the fact that you, as the player, are now controlling the incarnations, but in-universe it could be attributed to Odio’s presence inside of the incarnations giving them a power boost. There’s also the fact they can now cast Armageddon and completely end the universe, something Pure Odio can also do.