What happens when I play Hextech Ray on an Elder Dragon while Imperial Decree’s delayed trigger is active and I have an Immortal Phoenix in the Trash? Can I play Immortal Phoenix from the Trash?

You can.

Per the current rules, there is nothing that would stop Imperial Decree’s delayed trigger from triggering Immortal Phoenix. It is a triggered ability generated by a spell; it is attributed a kill action, and thus the spell that generated it will also be attributed the same kill action. The owner of Imperial Decree is the controller of the delayed triggered ability; the player responsible for the kill action is the one who controls the ability; and that same player is the owner of Immortal Phoenix in the Trash. Thus all three conditions for Immortal Phoenix triggering are complete, and it will trigger.