speaking from personal experience, i've gotten a somewhat soft and, i guess i'd call it a greasy feeling, from leather when i've treated it with neetsfoot oil. now, that being said, i believe too much of the stuff is not good for the hide. i think i've read that on here before. but i must have put on a healthy amoount to get the oily feel that you are talking about. someone else might want to weigh in.
as far as tanning goe, i believe that oil tanned leather is chrome tanned.
as an afterthought, you might want to look into pull up leather. it had a greasy feel to it, although i'm not sure how well it does being used as a garment leather.