Position an oven rack on the highest rung (4 inches from the element) and heat the broiler to high. Pat the shrimp completely dry with paper towels. In a medium bowl, toss the shrimp with 1 Tbs. of the oil, 1/4 tsp. salt, and several grinds of pepper. Arrange the shrimp in a single layer on a foil-covered rimmed baking sheet. Broil the shrimp until they’re pink on the outside and opaque in the center, 3 to 4 minutes.
Mix the tomatoes, feta, olives, capers, oregano, 2 Tbs. of the olive oil, 2 tsp. of the vinegar, and 1 tsp. of the lemon juice in a medium bowl. Add the shrimp; toss lightly to combine.
In a small bowl, use a fork to whisk together the remaining 2 Tbs. oil, 2 tsp. vinegar, and 1 tsp. lemon juice. Toss the greens in a large bowl with the vinaigrette. Season generously with salt and pepper and toss again. Divide the greens among four large plates. Top each portion of greens with equal amounts of the shrimp mixture and serve.