To update that:
1) Leaves Great Debate and becomes a lone Avari elf. Takes an interest in astronomy while wandering Middle Earth under the stars. (Season 2, Epiosde 3: The Great Debate)
2) Meets and befriends Dwarves of the Blue Mountains, learning metalworking from them. Recall that our Nandor don't have metalworking technology at all, so this is a very un-Avari interest for him to have - definitely sounds like something he'd get from the dwarves. Develops a rapport with Telchar of Nogrod, who was the armorer of Doriath and later makes the Dragon-helm for the King of Belegost. In Season 4, Telchar comments on how 'wrong' his swords are in a conversation with Fëanoreans, though the audience doesn't make the connection between Telchar's story and the elf from early Season 2.
3) Sees meteor fall in what will later become Lake Helevorn. Goes to investigate and finds meteoric iron. Learns to use this to make his black swords and/or galvorn. (This back story has not yet been shown or alluded to in any way)
4) While exploring Beleriand (in search of more raw materials?) comes across Nan Elmoth and recognizes its innate magic, leftover from Melian's proto-girdle. Becomes enamored with the place and wishes to make it his home. (Unshown)
5) Petitions Thingol for permission to live in Nan Elmoth, and grudgingly parts with the sword as payment. (Unshown)
6) At some point, the Sun rises. And he grumbles about his new Noldor neighbors when they arrive. *They* just took the land and didn't pay Thingol at all! (Sounds like this will be a real-time bit of dialogue in Season 5.)
So, it looks like we will need to find a way to incorporate items #3-#6 into our story this season. Some things to consider:
Is it important for the audience to find out all of these things? If so, in what order should they be revealed? Is there some other aspect of his backstory that needs to be brought up?
Does Eöl tell these stories himself? If so, who is his audience and what is his motivation? Is he telling Aredhel his background to gain sympathy from her? Is he telling Maeglin so that his son knows his heritage? Does he tell different versions to Aredhel and Maeglin?
Do others tell these stories about Eöl? If so, what is their motivation? Are they warning others off from the 'dark' elf? Are they explaining their own issues with him? Or do they support him, and are defending why he is the way he is? ('Others' could include dwarves or elves of Doriath or Fëanorean neighbors or even Men.)
Do we show these events in flashback? If so, how does that work? Very brief scene flashed up during voice-over dialogue? A 'memory' playing out when a character introduces the story? Or are these strictly verbal recountings with no visual component?
I do think it important that the audience get to know Eöl how and when Aredhel does. They should have as much information as she does, and there should be enough ambiguity that her giving him the benefit of the doubt doesn't appear overly stupid. So, the stories he tells her should focus on his resourcefulness at first - how he found the meteor, or how he made Nan Elmoth his home. And when he does talk about his grudges, his bitterness shouldn't be so obvious, but he should manage to present it in such a way that he very clearly is the wronged party, so he's fishing for sympathy, not painting himself as anti-social. Others can talk more harshly about him, but we should only hear their voices after Maeglin is born, when Aredhel is starting to realize that not everything Eöl has told her is fully honest.
