Ok first off Thor is a hybrid of Asgardian and Elder God genetics because Odin wanted a son who's power wasn't dependent on the Asgardian dimension. This aspect for the most part has been rarely seen or portrayed so we can now assume that Odin wanted a son with two sources of power.
Thor has always been a God of nature but for most of his life he's has focused on the "sky" aspect or his fathers side. Only recently are we seeing Thor use some form of "Earth" or mothers side of his power. To what extent this will develop into is unknown but he does not have Gaea's power he is only accessing it or is a conduit for it like the Odinpower.
Right now what powers Thor has or doesn't have is so vague and poorly defined we are only guessing. But the fact is Thor is a son of the "sky" and "earth", of the heavens and the world underneath it. This aspect should be played up more, Thor is one of the very few who has a legitimate connection to both worlds and should have a deeper more meaningful connection to the Gods and mankind then your typical mortal or god and for sure farmboy aliens. It's literally in his genes and also vaguely similar to another influential figure....
Farmboy aliens eh?
Thor would seem to be pretty close actually to current Shazam, as both powered up or are gods, and have access to use some pretty strong magic!