This is something I’ve always wondered about. Look on any world map, and you can see that the oceans are really one huge body of water. How is it determined exactly where, say, the Indian Ocean ends and the Pacific begins, or where, exactly, the Pacific meets the Atlantic at the southern tip of South America? Is it by latitude and longitude? If I stand at the southernmost tip of Chile (or Argentina), could I scoop up one handful of two oceans?
Good question. Sadly, there is no answer: The oceans are merely names for very general regions of a continuous body of water that doesn’t know or care what humans think. If you want to go to Tierra del Fuego and claim you can touch two oceans at once, go for it. Nobody will be able to say you’re a liar.
The CIA World Factbook demarcates the oceans pretty specifically. They draw the lines differently than I would; they include the Mediterranean and Black Seas as part of the Atlantic, but consider all water south of the Antarctic Circle to be something called “The Southern Ocean.”
The people who define this sort of thing are the International Hydrographic Organization.
The IHO publishes a document called Limits of Oceans and Seas, which you can download from this page (ref S-23).
To answer your question about Tierra del Fuego, the IHO says this:
The latest edition seems to be dated 1953, so a lot of the country names are out of date.
What other ocean would the Mediterreanean and Black seas be part of? 
It wouldn’t be part of an ocean, they’re seas.
Of course, the Med (like the Baltic) connects to the Atlantic, but the circulation is so low as to be negligible. Taken to the extremes, the Atlantic Ocean is part of the Great Lakes because the St. Lawrence River connects them to the ocean.
So, technically-- Atlantic Ocean. Practically-- of course not.
All non-inland seas are part of oceans, regardless of circulation. The Great Lakes are fresh water.
It’s like arguing that country X isn’t part of continent Y because it’s a country.
The Mediterranean, Black, and Baltic Seas are all connected to the Atlantic via sea level, salt water connections, thus they can be considered part of the Atlantic. Even if there is limited circulation, it’s still there. The Great Lakes are freshwater, are not at sea level, and are connected to the Atlantic via a freshwater river through which there is no circulation. There is really no reason to consider them part of the Atlantic.
All seas (except inland seas like the Caspian) are part of an ocean. It’s not an either/or issue. Seas are subdivisions of oceans. Saying the Mediterranean is a sea and therefore not part of the Atlantic is like saying Chicago isn’t part of the USA because it’s a city, not a country.