Using the trainer, I've collected 3 pieces of the blade out of sequence. Now my game is broken and wont close the quest, even though I have had the blade forged.
You can finish the game despite having collected the pieces out of sequence. Once you have all the parts (even if the quest isn't at that point), go to Anvil's Ford and talk to Ulthane. You'll get the reforged Armageddon Blade. After that, head back to Leviathan's Pass (?), and use the shadow realm current to get back up to where you found the (supposed-to-be) first blade part. Walk over to Azrael, and everything should be straightforward from that point on.
However, that ending doesn't properly proceed the quest line, and, at least in my case, it didn't get me the achievement for finishing the game on Medium. Mind you, I didn't get the achievements for the scythe and tremor gauntlet either, so...
If you're still early in the game, I strongly recommend considering to restart anyway. To everyone else: Do NOT collect any Armageddon Blade parts before you're told to!