What is the most powerful element of Julia's careless nudity on page 31 of George Orwell's 1984?
In this dream scene, there are two reasons why Julia's nudity is so powerful.
First of all, Julia demonstrates her complete and total disregard for the Party's rules and regulations. This idea is reinforced by words like "disdainfully," "carelessness" and "annihilate," which Orwell uses to conjure an image of rebellion in the reader's mind. As a result, the reader (and Winston) comes to see Julia as a liberated woman, completely free from the social constraints imposed upon herself and her body by the Party.
Secondly, a powerful element of Julia's nudity is Winston's reaction to it. Despite her beauty, for example, Winston does not feel any sexual desire towards Julia, as he comments:
It aroused no desire in him, indeed he barely looked at it.
That Winston fails to appreciate Julia's sexuality is significant because it demonstrates that his own sense of rebellion is far stronger. He can no longer repress his inner desire to rise up and overthrow the Party. As such, this dream of Julia's nudity represents a turning point for Winston and explains why he wakes up with the word "Shakespeare" on his lips. He yearns to return to the way life was before the Party when thoughts and actions were uncontrolled and natural. He cannot ignore this desire for a moment longer: the time to act is now.
First, may I suggest that you ask questions with chapter numbers rather than page numbers since we may not have the same editions of the book.
I am assuming that you are talking about the part in Chapter 3 where Winston dreams about the girl who seems very much like Julia (although he does not yet know Julia at this point).
In that dream, the most important aspect of the girl's nudity is the complete freedom with which she acts. She does not act all self-conscious like everyone else in the society. Instead, she seems to be able to do whatever she wants. This is a very powerful thing in a society where no one is able to just do what they want in a carefree manner.