Factors to consider: Possible PTSD or some other form of dissociative disorder due to childhood abuse
Ni: House uses primarily intuition to figure out what’s wrong with people. He can pull paradoxical information together to reach out-of-the-box conclusions that surprise other people, but are usually right. House is a believer in universal truths (such as, “everybody lies”) and comes up with systems to discover and apply them to situations (NiTe). If something isn’t important to House, he doesn’t do it (or does it reluctantly). He only really helps out at the hospital because he’s bored. House uses his team to bounce ideas off of them more than he does anything else. He uses patterns to figure people out –often not even needing to see the patient to diagnose them. House likes to talk in metaphors.
Te: House likes to be in charge. He hates being told what to do and often ignores people’s suggestions if he thinks their suggestions are unimportant. He deals in facts, logic and empirical evidence (though he doesn’t always need to see the evidence to diagnose). He speaks bluntly, sharply and doesn’t always pay attention to other people’s personal feelings. He doesn’t always think carefully before he talks, and ends up offending people. House is action oriented. He needs to multitask in order to settle his thoughts (whether that involves watching TV or playing with a ball). House wants immediate solutions and would rather take the quickest, most efficient course to finding a diagnosis than sit and theorize for longer than he has to.
Fi: House doesn’t care about standard protocol and doesn’t follow orders when he doesn’t see a good reason for them. He doesn’t feel guilty about breaking privacy rights if it can save someone. He frequently crosses conventional ethical boundaries because he defines his own moral code rather than relying on anyone else’s. Though he often seems heartless, he is extremely principled (save the life vs follow protocol/respect privacy rights). When emotionally compromised, House would rather seek to understand his emotions (and others) than he would receive comfort.
Se: House likes to write everything down on a white board to keep his thoughts organized (visual learning). He likes to move around when he’s thinking, and often walks back and forth through the hospital while working through his thoughts. House often disconnects from the physical world and occasionally seeks thrills. House does a lot of things on the spur of the moment, diagnosing a problem that may or may not be genuine just so he can test so see if it’s actually there. His goal is not to be careful, but to get fast results. When he’s not doing something he’s bored.
I see House typed quite frequently as an xNTP.
However… he can’t be xNTP because his method for diagnosing uses Ni predictions followed by Te testing of empirical evidence. He literally refuses to believe in anything that can’t be proved empirically. The xNTP claim does make sense to the extent that House often locks himself into his shadow functions (which, for an INTJ, are the ENTP functions).
And yes, the argument that House talks too much to be an INTJ is a valid argument. The only explanation I can give for this is that there are a number of INTJ-fetishizing screenwriters out there (Stephen Moffat among them) who try to write INTJ characters without fully understanding them. As a result, they end up writing a caricature, or a stereotype rather than a true INTJ.