In a medium bowl, combine the coleslaw mix, chopped cashews, and sliced green onions. Set aside.
In a small saucepan, whisk together the rice vinegar, soy sauce, hoisin sauce, brown sugar, garlic powder, and ground ginger. Heat over medium, stirring often, for 3 to 4 minutes, until the sugar has dissolved and the sauce has thickened slightly. Remove from heat.
Heat the oil in a large skillet over medium-high heat. Add the chicken strips in a single layer and cook, stirring occasionally, for 5 to 7 minutes.
Cook the chicken until it is golden brown and cooked through. The internal temperature should reach 165°F (74°C) when checked with a meat thermometer.
Pour the prepared teriyaki sauce over the chicken in the skillet. Stir well to coat every piece.
To assemble, lay a warm tortilla flat. Spoon about one-fourth of the teriyaki chicken onto the center.
Top the chicken with a generous portion of the cashew slaw.
Fold in the sides of the tortilla, then roll it up tightly from the bottom to enclose the filling. Slice in half and serve immediately.