Daniel Plainview I think Daniel is a perfect representation of an LIE as well as of anunhealthy self-preservationist Three. His mind and speech is layered with productive, effective action, and, using his Ni ('these people don't know the processes of how to get oil; hence, I will use my skills to get it for them'), sells himself in order to gain more oil, money, power and success.
H.W. Plainview He I found hardest to type, not least because he barely spoke. He might have been an SLI, but I really don't know.
Fletcher Hamilton Possibly an LSI; Plainview's semi-dual. He seems to sit on the sidelines, and aids Plainview is his endeavours to gain more oil. Much in the way an EIE king or queen and an LSI advisor might operate, Hamilton is essentially a faithful subordinate.
Eli Sunday As corrupt as Plainview, I see EIE as most likely. He serves only his own agenda, and uses Fe to a T in his church services. He seems to understand Plainview's way of success, something which I think would be evident in business partners. The passive and essentially weak Abel, Eli's father, is practically powerless against Eli, but his part is quite minor, so I won't bother typing him.
Henry Brands The guy who manages to fool Plainview into thinking that he's his half-brother, Brands is another one who's a bit of a mystery to me. I think it's most likely that he's proficient in but not valuing of Se; perhaps SEI.