There's no such thing as an oldest language.
Languages do evolve all the time, compare the English we speak today with the one Shakespeare or even Chaucer wrote their works in.
There are languages that are more conservative than other, though, in that they change a lot less in the same amount of time. A notable example spoken in Europe would be Icelandic, which is not too different from the form which was spoken as far a 1000 years ago.
So to answer your question, the oldest language would be the first invented by mankind, a language we have no idea how it sounded, nor its grammar, or anything, just that it was presumably spoken in Africa some 100,000 years ago, and it has than spawned all other languages that ever since appeared on Earth.