I agree that Winston's conflicts are both external (man vs society--i.e. the Party) and internal (Winston vs his conscience). The most interesting thing about the internal conflict in this text is that, for most of the book, it is half formed. Winston begins defying the party with only instinct and trace memories to guide him. He doesn't struggle within himself because he doesn't know who he is. For the most part, his struggle with the Party is also half-formed. I think this is part of the point of the novel: Winston does not know who or what the actual opposing force is, so he does not know who or what he should be in conflict with (yes, he understands that he should resist "the Party" and all that it stands for, but he does not know who, precisely, the Party is).
The overarching conflict is the individual(free will) vs. government(Big Brother). Throughout the novel, Winston struggles with whether or not he should continue with his own thoughts or adhere to what Big Brother tells him is true. In the end, he is brainwashed into buying into whatever Big Brother says. He gives up his right to free will because of his fear and pain. This conflict is in general an external conflict as we see Big Brother taking steps to ensure the cooperation of all its citizens (the televisions in homes, etc.), but the reader sees the conflict specifically as it's played out in Winston's mind, which makes it an internal conflict as well.
The internal conflict would be Winston against himself as he slowly but steadily defies the Party and it gradually grows. The external conflict would be with his individualism and the Party wanting uniformity.