Preheat oven to 350°.
Combine first 3 ingredients in a medium saucepan; bring to a boil. Cover, reduce heat to medium, and cook 10 minutes. Place spinach mixture in a colander, pressing with the back of a spoon until barely moist. Set aside.
Heat oil in pan over medium-high heat. Add onion and garlic, and sauté 3 minutes. Remove from heat. Add spinach mixture, rice, oregano, pepper, salt, and cheese, stirring until well-blended. Set aside.
Place 1 phyllo sheet on work surface (cover remaining dough to keep from drying); lightly coat with cooking spray. Working with 1 phyllo sheet at a time, coat the remaining 7 phyllo sheets with cooking spray, placing one on top of the other. Place a sheet of plastic wrap over phyllo, pressing gently to seal sheets together; discard plastic wrap.
Spoon spinach mixture along 1 long edge of phyllo, leaving a 2-inch border. Fold over the short edges of phyllo to cover 2 inches of spinach mixture on each end.
Starting at long edge with 2-inch border, roll up jelly-roll fashion. (Do not roll tightly, or strudel may split.) Place strudel, seam side down, on a jelly-roll pan coated with cooking spray. Score diagonal slits into top of strudel using a sharp knife. Lightly spray strudel with cooking spray.
Bake strudel at 350° for 35 minutes or until golden brown. Serve warm.