Cut steak diagonally across grain into 1/4-inch-thick slices. Set aside. Combine soy sauce and next 5 ingredients in a small bowl, stirring until cornstarch dissolves. Add steak; stir well. Set aside.
Heat sesame oil in a large nonstick skillet over medium-high heat; add onion, and cook, stirring constantly, until tender. Add spinach to onion, and cook, stirring constantly, just until spinach wilts. Set aside, and keep warm.
Add steak mixture to skillet, and cook 3 to 4 minutes, stirring constantly.
Wrap tortillas in wax paper or damp paper towels, and microwave at HIGH 20 seconds or until warm.
Top each tortilla evenly with spinach mixture, steak mixture, and mandarin oranges. Roll up, and slice in half crosswise, securing each half with a wooden pick.