This question relates to two debated points of English style: Who vs Whom (warning: silly but excellent explanation) and whether it is OK to end a sentence with a preposition (short answer: "yes — depending").
"Whom" is not common in informal (and American) English. Also, in informal English, you may end a sentence with a preposition. Consequentially, if you are going to use "whom", you already sound more formal and probably should not end a sentence with "to".
So a question such as
To whom are you speaking?
is natural, but formal. Most would instead say (some variation of):
Who are you speaking to?
By the same logic the natural, informal version of your example would be:
Who does the Islamic state sell their oil to?
As with many things, which you use depends on your audience. It can sound odd to be formal with friends and coworkers, but it can be similarly inappropriate to be too informal in business or professional communication.
However even this varies considerably in different parts of the world and different industries. As an American — or, more specifically, a Californian — I only use "whom" as an affectation to make me sound particularly formal (or British). Since I work in technology, there is no need for me to use it professionally, as technical communication tends to be informal. The only place I might use it is with legal documents, formal letters, or invitations to formal events.