[Inziladun]

Originally Posted by Kuruharan

The Pukel-men are presumably not the people whom we refer to as the Men of the Mountains/Oathbreakers/the Dead. (I might be wrong about this...another point for discussion?)

No, they were Drúedain like Ghân-buri-Ghân.

Originally Posted by Kuruharan

So the tall men from the East would, in this case, be the Men of the Mountains/Dunlendings who were wicked at heart. In this case the Dunlendings were invaders as well in their own right.

The forerunners of the Dunlendings, maybe. The UT chapter on the Drúedain states:

An emigrant branch of the Drúedain accompanied the folk of Haleth at the end of the First Age, and dwelt in the Forest [of Brethil] with them. But most of them had remained in the White Mountains, in spite of their persecution by later-arrived Men, who had relapsed into the service of the Dark.

Those 'relapsers' were seemingly the Dead Men of Dunharrow. Interesting that they rooted out the 'native' Drûgs, and their later kin complained of being similarly treated by Gondor and the Rohirrim.

Originally Posted by Kuruharan

But then who are the natives of Enedwaith? For some reason I think of them as being related to the Dunlendings.

UT also makes mention (The History of Galadriel and Celeborn) of Men living in Enedwaith. We know that there were already Men in Eriador who made contact with the Númenóreans when the latter returned to Middle-earth, and those were said to be of the same stock as the Edain who had crossed the Ered Luin in the First Age into Beleriand.
It was later, after the time of King Aldarion, that the inhabitants of Enedwaith (presumably those same peoples who had met the Núemenórean voyagers before) that became hostile because of the Ship-men's timber-cutting. The Númenóreans then started treating them as enemies.