So we have decided that Eöl is Avari, and thus his name 'the Dark Elf' will refer to that. However, as an elf of Cuivienen himself (rather than a descendent of Avari elves), he is directly related to elves among the Noldor and/or Teleri. We did not establish which in Season 2, but we do have the opportunity to clarify his kinship in Season 3, should we wish to. Certainly, his attitudes (towards dwarves, craftsmanship, family pride, etc) make him seem more akin to the Noldor. Curufin and Celegorm are furious with him for marrying their half-cousin Aredhel, and offer him plenty of insults and threats on account of that. So, having him be a half-breed Tatyar/Nelyar Avari would fit as someone the Sons of Fëanor could speak scornfully of (not that they need much excuse!), and his equal hatred for them being kinslayers can be in play. I think we can work with that.
As far as what we have of him so far...here is his role in Season 2 Episode 3 Act 3:
Eöl says his piece: He starts off calm but as he goes on he works himself up into anger. He says the Quendi are meant to be out in the woods of the world. He calls Valinor a cage and accuses the Valar of not caring and wanting slaves. Worse, they will keep us as pets! Míriel tries to calm him, but that only riles him
more. He is done with the lot of them and will leave. His parting shot as he storms away in fury is a warning that this will end in blood. He notices a large bat as he leaves.