Over a shallow bowl, cut the chicken with a pair of scissors into thin, lengthways, 1/4 to 1/2-inch strips. Halve the long strips across to give 2 shorter strips (to echo the size of the bell pepper strips). Don't get too hung up on precision, though; you're just trying to cut the chicken into uniform shapes.
Add the oregano, cumin, salt, sugar, 1 tablespoon garlic flavored oil, and the lime juice to the chicken. Stir to combine and let marinate while you get on with the onions and bell peppers. Preheat the oven to 225 degrees F if you wish to warm your tortillas.
Warm the peanut or olive oil in a large frying pan or wok and fry the onion slices over medium heat, stirring occasionally, for 5 minutes.
Spread the tortillas out on a cookie sheet and put it in the oven to warm.
Add the bell pepper strips to the pan with the onion and cook for 10 minutes. When both the onions and peppers are tender, remove them to a bowl.
Warm the remaining 2 teaspoons garlic flavored oil in the pan over medium heat and add the chicken with its marinade. Cook, stirring frequently, for 5 minutes. Check that the chicken is piping hot and cooked through, then add the onions and bell peppers. Stir together, then transfer them to a serving dish.
Take the warmed tortillas out of the oven and put them on the table alongside the chicken mixture and all the other accoutrements. Wrap what you fancy in the tortillas and eat straightaway.
Make Ahead Note:
The onion and bell peppers can be cut 1 day in advance. Cover tightly with plastic wrap and refrigerate. The chicken can be cut 1 day in advance and tossed with the oregano, cumin and garlic flavored oil. Cover tightly with plastic wrap and refrigerate. Add the lime juice and salt just before cooking.