I don't think that I have the sufficient information to type these people as for the most part I have seen them act in school or in battle where they had to conform to a certain code of a social ethic.
I would have to guess that Harry Potter is an Introvert. When he had free-time in school, an environment where he had many friends and an opportunity to socialize, he didn't bother. The environment encouraged him to socialize, yet somehow he consistently displayed a disinclination to do so.
I would guess that he also is intuitive as in friendly and laid back conversations with professors, he displayed an ability to connect ideas together well and also enthusiasm for doing so. Seems to me that this behavior came to him rather naturally.
Would also say Thinking type as in almost all situations where he was able to behave naturally, he sought for structure in notions as well solutions to various problems. Rather rarely he focused on personal sentiments or aesthetical impressions. Judging or perceiving, I would probably guess Judging, but this is the weakest of all inferences I am making. I am drawing this conclusion on the basis of how Intuition seemed his dominant function as he did not seem to be very fond of structured thought. Nor did he seem to be a T dominant, as he did not have this natural intense focus on the impersonal and the characteristic dryness we associate with T doms especially Ti doms. In that regard he contrasts with another character in the plot; Snape, whose normal mode of utterance was very sequential, carefully pondered, dry and as precise as possible. (One may argue that this is attributed to the fact that he is old and a professor rather than to his type, but I'd be inclined to think differently: other old professors did not have those characteristics. Its also the case that most of Snape's personal experiences weren't different enough from theirs to regarded as the sole cause of the significant differences in character between him and them.)