As early as the 11th century a dictionary of Turkish dialects (Diwan Lughat al-Turk) recorded pleated or folded bread as one meaning of the word Yuvgha which is often related to the word yufka which is often the word for a single sheet of filo.
Over time every chef out did the other by making the pastry thinner and thinner with more layers. The tissue thin filo dough of today was probably developed by the Ottoman Sultan's chefs in the Topkapi Palace in Istanbul.The idea of the thin dough came up through Turkey into Vienna during the late15th century.
Very probably when Austria was attacked by the Ottomans. You don't usually think of armies leaving dough when they attack, but armies moved much slower then, attacked and sometimes settled for a while then move forward again. It would seem only likely that you would look around and want your favorite foods! By the way the Ottoman's didn't take Vienna. The Turkish and Greek thin dough (Filo) is very different from a Viennese Strudel dough. They are tissue thin and the strudel dough is skin thin. The Filo or Phyllo uses a bit of shortening and touch of vinegar. During the Austro Hungarian Empire ruled by the Hapsburgs. Strudel dough was made so thin and flavorful in part the Austrian bakers say because of the great hard winter wheat in Hungary that has a high gluten content.
This dough was really versatile and could be used to make a very cheap and satisfying dinner with vegetables and scraps by rolling it up Jellyroll style much like in the hard times in the States Tuna pinwheels were invented. Times were very tough then and one of the most common foods in abundance was apples. Probably it was one of the ONLY foods they had to put into the Strudel .
The oldest recipe in the Viennese library is for a milk cream strudel. One of my dad's favorite deserts he remembers growing up at the Strudel fests was Cheese Strudel. It is like a cheese cake filling. This was one of the strudels his mother and the ladies of the German club all got together and made Strudel where they pulled the dough out over the dining room table "skin thin".
Most all information was obtained by The Oxford Companion to Food , and The Penguin Companion to Food by Alan Davidson
The dough has to really develop a lot of gluten and the recipe used an interesting technique where you
throw the dough down on a board on the flour 100 times.
Here is the recipe for Apfel Strudel my dad remembers as a kid.
Make Some Classic Apfelstrudel