How does fat affect gluten development in strudel/phyllo dough?
Fat can inhibit gluten development in things like cakes, where the fat is allowed to coat the flour before other liquids are added. In things like bread dough, it slows down the gluten development a bit, but since the flour has already come in contact with water, it doesn't stop it. In the context of your phyllo or strudel, the oil serves a couple of purposes. First, oil in a dough helps to keep it from drying out which is very important when working with such thin doughs. Second, adding oil to a dough can help to make it easier to handle (less sticky). 

The resting period of your dough both allows enzymatic reactions in the dough to further develop the gluten, and it allows the gluten to relax. You can think of the gluten as strings in your dough. As you knead the dough, you're winding these strings tighter and tigher, but when you let it sit, they can begin to stretch and loosen. This relaxation makes the dough much less "tight", so that it can be rolled out more easily without springing back as much.