Combine cabbage, cilantro, and salsa in a serving dish; set aside.
Cut chicken crosswise into 1/2-inch-wide strips. In a 10- to 12-inch nonstick frying pan over medium-high heat, stir oil, onion, and garlic for 2 minutes. Increase heat to high, add chicken, and stir often until meat is no longer pink in center, 4 to 6 minutes.
Add cumin and oregano; stir for 15 seconds. Spoon into a serving dish.
Wrap tortillas in a cloth towel and cook in a microwave oven on full power (100 percent) until hot, about 1 1/2 minutes. At the table, spoon the cabbage and chicken mixtures into the tortillas.
