He is too flamboyant to be an INTJ, and he isn't really very righteous. Also, I can't really see efficiency (Te) in him, he just doesn't come across as a product-oriented type, but rather, has a decently strong Ti. He seemed more amused and extroverted than a typical INTP, and also, he seemed to view everything as fun, seeing how he has a small smile on his face all the time. Besides that, he had a strong use of Ne when it showed that he even prepared a portal for Ichigo to rescue Orihime, and his movements, while being calculated, aren't actually very righteous/ethical motive, but more of a cause for amusement and to help out others.
Ichigo: XXXX never liked him, never will.
Rukia: ISTX/ INTJ
I originally thought ISTJ, since she seemed to carefully follow the rules and take after Byakuya, but her dominant function doesn't really seemed to be Si.
I can't tell. Sometimes, he surprises everyone by not upholding the rules, other times, he quietly uphold and submit. Probably INTJ, but he had a strong Te, just that it's not dominant.
She can burn herself, she's literally just there to cry, pretend to be innocent, and be a perfect character for fan service.
He is extremely loyal (Dominant Fi). Doesn't seemed to use Se very much, so I'll guess INFP.
He follows orders, but he's dominant function seemed to be Ti over Ni.
...I don't even need to explain, seriously, just look at him.
I can't be sure about Shinji.
Like what @Eska said, I wouldn't type him as an ESTJ since he doesn't impose anything on others. He punished them for breaking the rules because he is /obliged/ to. Also, it's clear that he likes to be alone, and he doesn't really like company, as seen from how awkward he gets around others.