Preheat broiler. Line large rimmed baking sheet with foil; brush lightly with 1 tablespoon olive oil. Arrange tomatillos, poblano chiles, cut side down, and garlic cloves on prepared baking sheet. Broil until tomatillos and chiles begin to soften and blacken in several spots, watching closely to prevent burning, about 10 minutes (do not turn). Remove from oven. Let stand until cool enough to handle, about 15 minutes.
Transfer tomatillos to processor. Peel garlic and add to processor. Peel charred parts of chiles; coarsely chop chiles. Add generous 1/3 cup chopped chiles to processor (reserve remaining chiles for enchilada filling). Add 2 cups cilantro and 1 cup green onions to processor; using on/off turns, blend until coarse puree forms. Season salsa verde to taste with salt and pepper. Transfer 1 1/2 cups salsa verde to shallow bowl.
Heat 2 tablespoons oil in large nonstick skillet over medium-high heat. Add chopped red onion and saute until slightly softened, about 2 minutes. Spring shrimp with salt and pepper. Add shrimp, oregano, cumin, and remaining chopped chiles to skillet; saute just until shrimp are almost opaque but not completely cooked through, tossing often, 3 to 3 1/2 minutes. Remove shrimp mixture from heat.
Preheat oven to 350°F Brush 15x10x2-inch glass baking dish with remaining 1 tablespoon olive oil. Spread 1/2 cup salsa verde fromprocessor in bottom of dish. Stack tortillas; wrap in damp paper towels and place on plate. Microwave tortillas on high just until soft and pliable, 1 to 1 1/2 minutes. Working with 1 tortilla at a time, dip tortilla into bowl with 1 1/2 cups salsa verde, turning to coat both sides evenly. Transfer to prepared baking dish. Place 4 shrimp and some onion-chile mixture down center of tortilla, then sprinkle rounded tablespoonful cheese over. Roll up tortilla, enclosing shrimp and onion-chile filling. Place seam side down in dish. Repeat with remaining tortillas, shrimp, onion-chile mixture, and cheese. Spread 2 cups salsa verde from processor over enchiladas.
Bake enchiladas just until heated through and cheese melts, about 20 minutes. Using spatula, transfer 2 enchiladas to each of 6 plates. Spoon any remaining salsa verde over; sprinkle with remaining cheese. Drizzle with crema and garnish with red onion slices and additional chopped cilantro, if desired.
Note: If the poblanos aren't hot enough, add some chopped jalapenos to the salsa verde. Garnish enchiladas with fresh avocado slices and drizzle with crema mexicana (a nutty cultured cream available at some supermarkets and at Latin markets) or stirred sour cream if crema is unavailable.