In a large nonstick skillet, heat the olive oil over medium heat. Add the scallion whites and cook, stirring, for 1 minute. Add the shrimp and chili powder, season with salt and pepper and cook until the shrimp are opaque, about 5 minutes; transfer to a large bowl.
Working with 1 orange at a time, slice off both ends. Stand upright and cut away the peel and pith, following the curve of the fruit. Slice along each membrane to release the segments, then coarsely chop.
Stir the mayonnaise and lime juice into the shrimp mixture, then gently fold in the orange segments and avocado; season with salt and pepper. Spoon the shrimp salad on top of the lettuce and sprinkle with the scallion greens.