For short, if someone buys physical oil, they need it for something. It is awful stuff, that really cannot be used for anything without processing (apart for being used as fuel in large vessels maybe). The sellers of oil are companies that have oil wells.
If you read about oil prices, it is like stated in a comment, usually the price of Brent or WTI.
The ICE (Brent) has an Exchange for Physical (EFP) delivery mechanism, with an option to cash settle. Hence there is no obligation of taking physical delivery.
WTI is physical delivery only, at any pipeline or storage facility in Cushing, Oklahoma with pipeline access to Enterprise, Cushing storage or Enbridge, Cushing storage. Cushing is the most significant trading hub for crude oil in North America, connecting the Gulf Coast suppliers with northern consumers.
What type of oil to deliver is also tightly regulated by chapter 200 of the rule book. It must satisfy certain criteria with regards to sulfur, gravity, viscosity, reid vapor pressure, basic Sediment, water and other impurities, pour point and so forth.
However, there are numerous other places where oil is drilled and stored and various qualities. Canada has readily available quotes for Central Alberta, Light Sour Blend, Peace Sour, Syncrude Sweet Premium, Sweet Crude, US High Sweet Clearbrook, Midale and Albian Heavy Synthetic for example. Oilprice.com shows 15 quotes for Texas alone (click on the dropdown next to United States Blends in the menu on the left). There are several regions though.
Oil wells exist in a vast number of countries, like UAE, Kuwait, Qatar, Iraq, Iran, Saudi Arabia, Nigeria, Australia, Mexico, China, Russia, Venezuela and Malaysia to name a few. Tower 1 of the iconic Petronas Towers in Kuala Lumpur is fully occupied by Petroliam Nasional Berhad (National Petroleum Limited), commonly known as Petronas, a Malaysian oil and gas company wholly owned by the government of Malaysia.
If you buy oil from them, you buy from the Malaysian government. If you buy oil in the US, there are hundreds, if not thousands of companies engaged in the exploration and production (called upstream) of oil, with the majors being BP, Shell, Exxon Mobil, Chevron, and Total. In this case, if you buy oil, the proceeds directly go to these firms.
Who buys oil (if not you)? Raw oil needs to be refined, so it ends up at a refinery (called midstream) before going to be distributed as different products to various customers. Ultimately, the demand for this comes from the final customers though. These could be car drivers, airlines, petrochemical producers and the like.
Therefore, unless you know exactly where and what oil you are interested in, it is impossible to say who produced it, and who will usually buy it.