Firstly, as to Odin dying in Ragnarok, yes, he does. The Fenris Wolf (and I much prefer this less common spelling of the name) devours him, but he is avenged by his son Vidar the Silent. But whoever said it is wrong in saying that all perish in Norse: Baldur, Hodur, Magni, Modi, Vali, Vidar, and a man and a woman, at least, outlive Ragnarok and see the new earth... or so says Odin's vision of the future.
When I said "Stated Gods" I ment like entitys. The Dragon God's are not.
And I'm pretty sure all Greek God's were immortal forever, and could not even die by a weapon. Norse God's were capable of dying. The Greek's had the river Styx to bathe in (like Achellies, but he was the Son of a God and a human, so he had to be bathed in it to have immortality). The God's were born with immortality, but I'm just guessing that only their parents could destroy them, in other word's the Titans and Kronos, but even then they still did not die, only Zeus had to kill Kronos and then Hades/Posideon came out.
Norse... yes and no. Baldur died, as did his brother Hodur to Vali the Avenger, it is true, but were they not fated to be amongst the few to arise after the fiery doom of Ragnarok? The others who actually die, as opposed to simply being cast into Helheim for the ages of the world, do so in Ragnarok itself, which is an extrodinary circumstance where most everyone, gods, men, and giants, die.
As for Akhilleus (this is my preferred way of spelling it, as it is most true to the actual way), I think, if I remember right, he was never immortal in Homer. He was simply the greatest warrior whom none could overcome, and it took later writers to invent the whole tale of immortality, and his dip in the Styx - by whom the Gods swear unbreakable oaths - which bestowed upon him his charméd life.
As for the immortality of the Greek gods, see the next reply of mine.
No even the Greeks had legends about stuff that could kill the gods.
As far as things and weapons, none per say that I can think of. The nearest is the very sickly by which Kronos castrated his father Ouranos, usurping his place of heavenly command, but this did not utterly destroy Ouranos. Likewise Zeus overcoming Kronos did not destroy him, and some even have Kronos being the lord of paradise, in exchange for his heavenly throne. Atlas, also defeated, bears the world on his shoulders. And so forth. You see, the gods are in command of death (Thanatos, or the Grim Reaper as we would know him) and the underworld Hades, or more properly the realm ruled over by Hades, which consists of several areas. What these are vary from myth to myth, but some take an anvil falling from Olympos to take seven days to fall to the earth, and from earth to Hades seven days, and from Hades to the pit of Tartaros seven days. Thus Tartaros is the deepest, and that is hell, where the evildoers are punished, and some of the Titans (the 'Strechers') imprisioned. But as I said, no weapon I can think of per say can do it, save that in some myths the gods may indeed be harmed.
Homer, however, does allow for the gods to be injured, yea even by mortal heroes. Diomedes, near my favorite of the warriors of the Trojan war, wounds first Aphrodite, spilling her blood (that is, ichor, for she is a goddess), and later that bloodthirsty butcher Ares himself. In fact, when Aphrodite complains about Diomodes and his arrogance in injuring her, she is told that at whiles all of them have been in danger of injury, and it even seems that Ares was at one point imprisioned in a bronze pot (or something like that), and was in danger of death. Interesting, indeed.
Overall, though, one must remember that the Greek myths are not one set saga. Rather, they are the collective tales of many disparate regions and peoples over a period of almost a thousand years. Not only do they change, but different areas have different views (who was Zeus' wife? Hera? Metis? Leto? Most modern retellings make them successive, to clear the confusion that comes about from these different regionalities.) So it cannot be conclusively known how immortal they were, as different areas and times have different ideas.
And finally, as for Prometheus... yes he was a Titan. But one must remeber, what makes a Titan, and what makes a god? Are not the Olympians the sons and daughters of Titans? Titan simply means 'Stretcher', for to Ouranos, when he was usurped by Kronos, it seemed that his offspring were over-reaching their power and authority. Thus that generation of gods were known as Titans, but in inherent make-up, they are no different than each other. All these, whether it is Hades or Zeus or Erebos or even Styx, they are all gods of a similar sort, and almost always related.
By the way, Prometheus means 'forethought'; his brother's name, Epithemus, means 'after-thought'.
