I'm currently playing a role-playing game as a cleric that worships a god of storms and I'm researching what kinds of offerings that god would likely accept.
What examples are there of the kinds of offerings that were made to Thor?
Blood and poetry.
Before I go any deeper, I want to clear up a misconception: Thor is not really a god of thunder. Yes, he does generate it, but his main function is as guardian against the forces of chaos (which goes directly against how gods of thunder storms are portrayed in some RPGs).
The main sources for the worship of the Norse gods are the Icelandic sagas and archaeology. The latter is not very good for discerning differences between different gods, and the former is also not very reliable. Thor is actually a prominent god in these. I will give two examples.
In the Saga of Erik the Red, at one point the Norse explorers are starving. One man, Thorhall, makes an offering to Thor of some poetry he has made, and soon after, a whale is beached. When Thorhall claims that it was due o his offering, the rest of the explorers, who are good Christians, refuse to eat any more.
In Eyrbyggja saga, Thorolf Mostrarskegg is a follower of Thor who moves to Iceland. He constructs a new house for himself, with a hallowed side room. In the middle of this was an altar, with an arm ring. This ring was used for swearing all oaths, and was worn by the cult leader at all sacrifices. There was also a vessel with blood from sacrificed animals, which could be sprinkled in rituals. Thorolf also hallowed a mountain, on which you were not allowed to look unwashed, and not kill people or animals.
As the mountain can be a bit unwieldy an offering, we can also take a third example, of a worshipper of Frey: The titular character of Hrafnkels saga Freysgoða has a horse hallowed to his patron, one which he has sworn that he will kill anyone who rides it apart from himself, which of course happens and drives the action of the story.