who are the nazgul?

[Zigûr]

The Nazgûl were not all "kings," just powerful leaders of Men.
In "Of the Rings of Power and the Third Age": "Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old." (emphasis mine) Evidently some of them only became kings after they received their Rings, and some may never have specifically been kings at all. If the Númenórean Ringbearers became kings, it might have been, for instance, in Númenórean colonies in Harad, given that they obviously weren't kings in Númenor.

Three were Númenóreans, as is stated in "Akallabêth": "Yet Sauron was ever guileful, and it is said that among those whom he ensnared with the Nine Rings three were great lords of Númenórean race." The Lord of the Nazgûl was probably one of these Númenórean lords, but we don't know for sure.

One, as you say, was an Easterling - Khamûl.

The rest we don't know, but if there were only three Númenóreans the rest must surely have been Easterlings or Haradrim. Given how long Sauron spent in the East and how long it was under the shadow it seems extremely likely to me that several of the Nazgûl were probably Easterlings. I suppose some of them might have come from the Men who dwelled in western Middle-earth in the Dark Years but in my opinion they always come across as too primitive and disorganised for there to have been much point in Sauron giving any of their leaders Rings.