[denethorthefirst]

There are probably several dwarven kingdoms in the east. We know that all the dwarven houses united to fight the orcs of the misty mountains in the war of the orcs and dwarves. Since the only dwarven states/groups that are mentioned in the west are those in the iron mountains, the blue mountains, erebor and moria the remaining houses must have come from the east. If I remember correctly four of the seven dwarven houses originated in the east. Considering that Sauron couldn't conquer Moria I guess it's likely that these dwarven pockets survived during the second and third ages even though Sauron ruled the surrounding areas.

I always wondered what happened to the Avari. It's possible I guess that they prospered relatively uninterrupted in the first age while Morgoth was locked up in the North during his war with the Noldor. Luckily for the Avari he wasn't in a position to divert much of his attention to the rest of arda during the wars in Beleriand. Maybe the Avari built several great kingdoms, or maybe they lacked the population numbers and necessary culture to built successful states and got annihilated in wars against dwarves, men and morgoths surviving monsters from his days at utumno.
At least by the time of the second Age, when Sauron expanded eastwards, the peaceful time for the Avari probably ended and they were either enslaved or hunted down.