An Me 262 uses at most 1,600 liters per mission. A few hundred Me 262s each needing 400 gallons per mission (including training missions) is hardly ASB-land. Any one of these *might* work, or you could use them in combination.
* They take it from the rest of the Reich, prioritizing stopping Overlord over something else (like the V-weapon program, or the submarine program, or ...). For just one example, an Me 262 has 1,800 liter tanks. An Type VII submarine holds 67 tons of fuel. You can fuel 34 Me 262 flights for one sub mission.
* They get it from Spain/Switzerland/Sweden/Turkey, who is allowed to import more oil for diplomatic reasons.
* They get it from Norway, where some of the offshore oil fields are on shore.
* They get it from Romania, where minor technological changes allow a greater percent of the in ground oil to be extracted.
* They get it by converting coal.