Blue: You see these guys at the beginning of Cairo. Pretty weak.
Red: You see these guys a lot on Cairo. Stronger than blues.
Black: Seen only as allies when playing as the Arbiter. Seen in The Arbiter and the beginning of Uprising. In Oracle he's the ally with the single plasma rifle.
White: Really strong, seen alot on Legendary, and at the end battle of Gravemind.
Gold: These guys only use swords in Halo 2. Seen as an ally in Uprising and at the end battle of The Great Journey.
Dark Blue: Seen everywhere in Gravemind. About the same strength as black elites. In Oracle he's the one with dual plasma rifles.
Gray: These guys are invisible. You see them mostly in Gravemind.
Brown: Also invisible, stronger and less common than grays. You should see one under the armory in Cairo.
Red Honor Guard: You see these guys at the very end of Delta Halo. Pretty tough.
White Honor Guard: At the very end of Gravemind you should fight one. He has a triangle-shaped crest. You see a lot of ones without crests in Gravemind.
Councilor: About the same strength as white elites. They're your allies later in The Great Journey, and have rounded crests, similar to the white honor guard crests but not the same.
*I don't count the Spec. Ops. leader as an elite type because there is only one of him, or the flying Rangers because they don't behave like normal elites.