Specifying which nations claimed the oregon country?

The region was occupied by British and French Canadian fur traders from before 1810, and American settlers from the mid-1830s, with its coastal areas north from the Columbia River frequented by ships from all nations engaged in the maritime fur trade, most of these from the 1790s through 1810s being Boston-based. 

Convention of 1818 

John Quincy Adams was central in crafting the Convention of 1818. Even though called a "convention," this was actually a treaty. 

The Oregon Territory -- essentially the Pacific Northwest from the Rocky Mountains to the Pacific Ocean and extending both north and south from the 49th Parallel -- was rich trapping and trading ground for both the U.S. and Great Britain. It also contained vital Pacific ports. 

In a remarkable step, the two nations agreed to hold the territory jointly for at least ten years, then go through a diplomatic process to divide the territory when one country or the other was ready. In essence, the countries were disavowing warfare as a method of deciding who would get Oregon. The Convention also set the U.S.-Canadian border at the 49th Parallel from the Lake of the Woods to the Rockies.