Preheat a grill to medium high. Toss the shrimp and onion in a bowl with the olive oil and oregano. Season with salt and pepper.
Stretch the pizza dough into a roughly 8-by-10-inch rectangle. Lightly brush the grill with olive oil. Lay the dough on the grill and cook until the top begins to bubble and the bottom is marked, about 3 minutes. Remove with tongs and put cooked-side up on a cutting board. Brush with olive oil.
Grill the shrimp and onion, turning, until the onion softens and the shrimp are lightly charred, about 5 minutes. Top the crust with the shrimp and onion, then slide the pizza back onto the grill. Top with the tomatoes and feta, cover and grill until the dough is cooked through and the cheese is soft, about 5 more minutes.
Carefully transfer the pizza to the cutting board. Sprinkle with the parsley and cut into pieces.
Per serving: Calories 585; Fat 28 g (Saturated 7 g); Cholesterol 143 mg; Sodium 708 mg; Carbohydrate 60 g; Fiber 3 g; Protein 27 g