I thought only Thor, Odin, Valkyrie, the Executioner, and Balder had weapons of choice, really. Thor had Mjolnir, Odin had Gungnir, Valkyrie had Dragonfang, the Executioner had the Bloodaxe, and Balder had the Sword of Frey (at least during Simonson's run, although everyone's probably forgotten that by now). Hogun had that spiked mace, but I don't think it was a special weapon in any way. A crapload of Asgardians all used swords too, so it's not even like each of them had a unique type of weapon. Although I guess JMS could easily just make up magic weapons and say the Asgardians had them forever but just never really talked much about them. Which I would surprisingly be fine with. I've always thought Asgard could use more magical weapons.
I can see JMS going into the real Norse Legends where there are alot of gods that have a specific weapon they use. I can't really think of any at the moment but I will check out some of my texts and sagas and find some examples for everyone besides the ones we know. And I really hope Thor kicks Tony's ass. He totally deserves it.