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Διὸς δ' ετελειετο βουλή · 5 εξ οὑ δη τα πρωτα διαστητην ερισαητε
Ατρεϊδης τε Ϝαναξ ανδρῶν και δῑος Αχιλλεύς.


In the first sentence, Dios with a downward accent relates to Zeus, head God, but in the second sentence, dios with an elongated "iota" relates to being Godlike in relation to the following word for Achilles, why?

Well done identifying the different accents. That's the key. You've stumbled across two different (although related) words.

The first is the genitive of Zeus - an irregularly declined proper noun (see Smyth 285.12 for full declension). The accent points down (grave) because another word follows it. Otherwise, it would point up (acute).

The second is an adjective meaning "divine" or "god-like." The circumflex (represented here by the horizontal line) indicates that vowel contraction has taken place. The word is derived from the first and is etymologically diios [sorry for the crappy transliterations but I don't have very good unicode-typing capabilities on my pc.] It is a nominative singular - modifying Achilles.

The best way to tell the difference (besides the context) is by the accent - as you managed to do. In edited texts, the capitalization of the Dios indicates it is a proper name. This is why editing texts from manuscripts (that had no punctuation, accents, etc.) can be so tricky.

Homer is tough, but you seem to be doing okay.