The government of Turkey. Though this is hotly contested, there is some direct evidence and much circumstantial evidence to suggest that the Turkish government has at the very least facilitated/mediated the purchase of oil from IS (if not actually buying oil itself).
Oil tankers - illustration
The basic circumstantial evidence:
- The oil exports can (technically) happen by land, sea, or air.
- They're not happening by air: IS has no air force or civilian air fleet; and this would very likely have been subverted; and it's probably not even economically viable at all.
- They're not happening by sea: IS territories in Iraq and Syria are land-locked. (Syria isn't; and Iraq isn't - but coastal areas have been held by the respective regimes and never by IS).
- The forces/terriories surrounding IS lands with oil in them, are: Turkey (now through Turkish-backed Syrian Islamist rebels, but until the Turkish invasion last year it was Turkey proper), Rojava (Kurds/SDF, northern Syria), Kurdish Regional Government (northern Iraq), the Iraqi state regime, the Syrian state regime, non-IS Islamist rebels (Idlib area, Joulan area, near Jordanian border), Jordan. Israel borders an IS-controlled area directly but it's a small enclave so no oil could through there except through non-IS Islamist rebel territory before.
- It's extremely unlikely the non-IS and IS Islamists would cooperate clandestinely in oil trade without this being found out, and when they're so much at odds otherwise. In fact, it's highly unlikely they would cooperate at all.
- No evidence of significant collusion of any of the above-mentioned forces/states, except Turkey, with IS or IS personnel in those areas. (this is a weak point since I've not extensively looked for such evidence.)
- Lots of news stories over the past several years on IS activity in Turkey, people and fighters crossing the Turkish border back and forth, IS recruitment in other countries inviting people to meet in Turkey etc.
- A relatively authoritarian regime in Turkey which has acted brutally against civilians in its own territory with significant military presence in Eastern Turkey. So - relatively easy to carry out secret activities without public oversight or unusual vehicle and troop movements.
- No way you could send oil tankers over a state border regularly without the state allowing this to happen. Once or twice - maybe you got away with it; a barrel here or there - possible to smuggle I guess, but that does not allow for a real flow of oil. It must be tankers, wherever the oil goes.
- Iraq has its own oil sources (the KRG as well), so they wouldn't need to rely on IS oil. Syria - not sure about domestic oil production, certainly with the war, but they definitely have easy access to the Mediterranean.
So, circumstantially, which would be the most likely culprit? Turkey.
Now, as for proper evidence, I'm quoting from this blog post:
The Guardian reported:
US special forces raided the compound of an Islamic State leader in eastern Syria in May... The target ... was an Isis official responsible for oil smuggling, named Abu Sayyaf. He was almost unheard of outside the upper echelons of the terror group, but he was well known to Turkey. From mid-2013, the Tunisian fighter had been responsible for smuggling oil from Syria’s eastern fields, which the group had by then commandeered. Black market oil quickly became the main driver of Isis revenues – and Turkish buyers were its main clients.
... In the wake of the raid that killed Abu Sayyaf, suspicions of an undeclared alliance have hardened. One senior western official familiar with the intelligence gathered at the slain leader’s compound said that direct dealings between Turkish officials and ranking Isis members was now “undeniable”.
Al-Monitor quoted a member of the Turkish opposition party CHP (the secularist/nationalists/militarists/Kemalists):
Opposition MP says ISIS is selling oil in Turkey
The Islamic State of Iraq and al-Sham (ISIS) has been selling smuggled Syrian oil in Turkey worth $800 million, according to Ali Ediboglu, a lawmaker for the border province of Hatay from the main opposition Republican People’s Party (CHP).
The Kurdish Daily News, quoting ANF news, reported
Sadik Al Hiseni, the head of the security committee in the city of Diyala in Iraq, says they have arrested several Turkish tankers trying to take ISIS oil out of the province of Salahuddin.
And you can find lots and lots more by web-searching.
Edit - July 2017: Turkey no longer has any border with the Islamic State, So obviously no sales since the cut-off; but the sales may well have ended before that. Probably even sometime before the Turkish invasion of North Syria.