What is the hierarchy among the races and within the world of Middle Earth?

I am not sure that the novel implies any sort of heirarchy between races - there is no information given of how races are viewed in relation to their being superior to other races. However, your question does raise an interesting theme of the story which is explored in its pages, particularly in the second half, which deals with the presentation of race.

This novel does focus on the difference between the major races. Each race have their own characteristics - physical, moral and psychological. Note too how races are grouped by the simplistic terms "good" and "evil". All goblins and Wargs are evil, and elves, dwarves and men are good. You might also want to think about races and their relation to nature. The "good" races are depicted as living at harmony with nature whereas the evil races pit themselves against the forces of nature. Consider the eagles' decision to join the "good" side at the end of the novel, for example. Thus race is of course a vitally important concept in the novel, and Tolkien gives us carefully detailed and individual races with their own separate and easily-discernable characteristics, but there is no sense of heirarchy implied apart from a simplistic grouping of races into two categories: good and evil.