You won't find it in the NEC. Here is what the letters mean:
Wire & Cable Type Description
T= Thermoplastic insulation
H= 75?C (Note: lack of "H" indicates 60?C)
HH =90?C
N =Nylon jacket
W =Moisture resistant
R =Rubber insulation
U =Underground use
USE =Underground Service Entrance *
UF =Underground Feeder *
SE =Service Entrance *
-2 =90?C and wet
Oil is not an official criteria. However there is nothing to stop a specific manufacturer from also including oil and gasoline resistance as part of their labeling. In the case of THHN and THWN, that was the initial reason they were developed; the "N" for Nylon was intended to provide protection against abrasion when being pulled in conduit but also against incidental contact with oil and gasoline when used in automotive service stations. But that was not laid out in the NEC. The only thing I have seen that addresses it is UL, so when they UL list their wire, UL has test criteria for "Oil Resistant" if you want to put that into your listing. As I interpret it though, you can get wire UL listed as THHN or THWN without also getting Oil Resistant added to it. That means if you bother to go through the expense of the test, you are most likely going to emblazon that fact right on the jacket and charge a little more for it, so it can be assumed that if it doesn't say it, it probably isn't.
I have a copy of UL-83, but to protect the site, I won't paste in the test criteria. However in a paraphrase, it is "Oil Resistant" 75C if after being submerged in oil for 60 days at 75C, the nylon jacket is intact, the insulation has not elongated (thinned) to less than 65% of it's original thickness (which addresses the dielectric strength) and has not lost it's tensile strength.