Thor is an Asgardian. Are Asgardians powerful enough to hold an Infinity Stone? Similarly, being gods, will Odin, Loki or Heimdall be able to wield any of the Infinity Stones?
It depends on which media continuity you're discussing. In the comics, he did use an Infinity Gem. In the movies who can use them seems to vary widely but he does seem reluctant to even consider using one, even when one falls directly into his hands (the Mind Stone from Avengers: Age of Ultron)
In the Marvel Comics Universe, Earth-616, the answer is yes. He has and did use an Infinity Gem. He, for a time carried the Infinity Gem of Power and confronted the Mad Titan, Thanos in hand to hand combat. Thanos cheats, which meant he was impressed.
During the Blood and Thunder storyline, Thor Odinson gets the Infinity Gem of Power and goes on a rampage across the Marvel Universe. Thanos and Thor mix it up in Silver Surfer Vol. 3, Issue 88. Thor, who is significantly more powerful than Ronan with the Universal Weapon, was now enhanced further with the Power gem. Thanos was unimpressed.
Thor plus Power Gem should equal oblivion for anyone on the receiving end of Mjolnir. Thanos has a bloody nose and smiles. Scary.
- In Marvel Cinematic Universe, their use criteria varies from stone to stone and user to user.
Of the Infinity Stones we've seen in the Marvel Cinematic Universe, thus far, none seem particularly user-friendly. The least dangerous of the group so far has been the Mind Stone, which was housed in the Chitauri Scepter.
The Power Stone (currently on Xandar) destroyed most beings who dared to maintain contact with it for too long.
The Aether seems to consume the host foolish enough to want to stay in contact with it. Judging with the speed the Asgardians got it our of Asgard, it is something to be avoided at all costs.
The Tesseract seemed pretty tame and it seemed to take a bit of Tech to get it work just right. Except when it appeared to disintegrate the Red Skull. Now we know he was probably teleported across time or some other ridiculous trope but that's it looked like.
In the Marvel Cinematic Universe, probably not - at least, not with his bare hands.
We don't know for sure as we haven't seen an Asgardian attempt to pick up an Infinity Stone with their bare hands - but the fact is whenever we have seen an Asgardian move an Infinity Stone, the stone is in a container so that they do not have to touch it.
We have seen this twice - when Thor and Loki return to Asgard at the end of The Avengers/Avengers Assemble with the Tesseract, and when Lady Sif and Volstagg deliver the Aether to The Collector at the end of Thor: The Dark World.
Additionally, in the Agents of SHIELD season 2 episode "Who You Really Are", we see that Lady Sif is roughly as strong as the Kree warrior that she is fighting. In Guardians of the Galaxy, we see that another Kree (Ronan the Accuser) is not able to hold the Power Stone for very long before having to embed it in his warhammer. If Kree and Asgardians are roughly as powerful as one another, we can assume that Asgardians can hold the Infinity Stones for about as long as them - which isn't very long at all.
In a slight counter argument, I'd like to think that Thor definitely can, as in the last Avengers film we are shown the Vision using the infinity stone within Loki's Sceptre to power himself, and he seems to be in control of it. So its far more than plausible they can, they are gods after all, and if the Vision can wield Thor's hammer, Thor in theory would be able to withhold the power of an infinity stone?