Now, alduce me to inTrolow myself. Sorry. Allow me to introduce myself. I'm Hacbad Macbar. I'm afraid I must ask that no one leave this room. This room is surrounded by sketch. If you leave the room, I shall leave the room. So, nobody leave the room till the sketch is goone. Sorry. Gone. With the wind.
Is this show still on? I can see ENTP for MBTI type, though as far as Jung he's a quintessential Introverted Thinker. He rationalizes in his head all day and comes up with his own questions and answers while ignoring most of the outside evidence and reasoning brought to him. He likes to get personal with his own investigation. It's not independence that characterizes an Introverted Judging type, but something more personal than this, individualism.
While he may be a P in MBTI (casual and unplanned), he's a J in Jung, someone who makes snap reactions and judgments as information tempers his certain value system, not like a P where information is merely thought and naturally allows itself to settle into clarity. But this could be based on Hugh Laurie who adds this J flavor to his character, as well as his relaxed Introverted Thinking pensiveness.
Extroverted Feeler as his dual makes a lot of sense too, perhaps someone lighthearted who's easy to bounce screwy sentiments off of without taking him too personally and serious.
So, maybe he's an ENTJ, but, ENTPs are abrasive too, and one is for sure (I think): he's more extroverted than introverted. He can be any of NT types. And, I don't know which one is he, exactly. Sometimes he behave like an ENTJ, sometimes like INTJ or ENTP.
But, what you think about his other characteristics/options from the questionnaire?
Because he's a fictional character, he actually embodies both the qualities of the ENTP and the INTJ, which actually plays a bit of a straining role in the show itself as a struggle between his anima and his demon, which is more controversial over which is which, though I would conjecture the roles are as follows.
Anima Si - Represented by Cuddy and the need for comforting and stable surroundings to distract him from his leg pain (the show's personification/symbol of his melancholic, highly dark Fi), but makes him much less precise and incapable as a doctor for some reason, as if his abilities are stifled (suggesting perhaps Ni is the source of his abilities)
Demon Se - Represented by his Vicodin abuse, as it allows for immediate pain relief and strengthens his abilities as a doctor while making him clearly "objective" and somewhat unfeeling (Ni/Se axis, presence of Se strengthens Ni's work); in fact, in one of the later seasons, his addiction embodies a mental projection of a certain ESTP that represents his scarily dangerous unconscious that attempts to subvert him and destroy him (which sounds more Demon than Anima).
The show, thus, revolves around the struggle of a deeply shadowed House attempting to figure out his dual inferiors, which clash and war throughout the series.
EDIT: It might be interesting to think that Ni Anti-Hero complex would actually manifest itself as the Hero function for House, as he is sort of an Anti-Hero in the first place. Perhaps his Si is his demon and his Se is his anima that was trying to save him from disconnecting himself from his Ni through Si demon integration.