The U.S.? No. The U.S. never actually declared war on the Ottoman Empire, though they broke off ties in 1917. U.S. oil production was a massive portion of the world's production, but virtually all of the world's oil shipping tankers at the time were owned by Britain.

The British (and to a certain extent the French) interest in Ottoman oil was more significant. Initially the most important consideration was securing the shipping routes for Persian oil that went through Basra. This was essential because the Royal Navy had been largely converted from coal to oil over the course of the past decade or so and the primary source of the Navy's fuel was the Persian oil fields.

The British declared war on the 5th of November 1914. On the 6th of November they landed at Fao on the Persian Gulf in the far south of Iraq. By the end of the month they captured Basra.

Oil played comparatively little role in the war from 1914 until practically the war's end. The most important (suspected) oil bearing region at the time was in Mosul Province, which is to say Mosul and what is today commonly referred to as the Iraqi Kurdistan province. The British government issued explicit orders to the field commanders in Iraq at war's end to seize these areas. In some instances this involved attacking and capturing positions in violation of the armistice. The armistice arrived on 30 October, the local commander captured Mosul on 1 November, for instance.

This region in particular was important for the post-war settlement. Under the Sykes-Picot agreement, Mosul province was supposed to go to the french. You can see how different the border of northern Iraq looks on the agreement here.

The negotiations between the French and British in order for Mosul Province to become part of the British Mandate for Iraq basically involved limited concessions to the French for stakes in whatever oil was found there.