In a medium bowl, combine the pork and marinade ingredients; toss well to coat and set aside.
PREPARE THE STIR FRY SAUCE:
In a small bowl, whisk together the stir fry sauce and set aside.
STIR FRY:
Heat a nonstick wok or a large, deep skillet over medium-high heat until a drop of water sizzles. Swirl in 2 teaspoons of oil, then add the pork mixture. Stir-fry until just cooked through, 4 to 5 minutes; transfer to a plate. Swirl the remaining 1 teaspoon oil, then add the mushrooms, ginger and garlic. Stir-fry until softened, 3 to 4 minutes. Add the cabbage and water; stir-fry until the cabbage wilts and is crisp-tender, 2 to 3 minutes. Add the green onions, pork and stir fry sauce. Cook, stirring constantly, until the mixture boils and thickens, about 1 minute.
ASSEMBLY:
Wrap the tortillas in a damp paper towel and microwave until hot. Spoon about ⅔ cup of the pork mixture onto each tortilla, roll up and serve.