Place avocado, onion, tomatillos, jalapeno pepper, cilantro, garlic, and salt in the bowl of a food processor. Pulse until small chunks remain.
Fill resealable plastic bag with shrimp, chili powder, and salt; shake to coat.
Heat olive oil in a skillet over medium heat. Add shrimp and cook until pink and opaque, 2 to 3 minutes.
Divide salsa, shrimp, and cabbage evenly to fill tortillas. Squeeze lime juice onto each taco.