Preheat a grill to 450 degrees.
While grill preheats, cook the orzo according to package directions. Also, in a large bowl, whisk together the olive oil, lemon juice, lemon zest, and dill. Season with salt and pepper. Set aside.
Place shrimp in a medium bowl and drizzle with olive oil.Season with oregano, salt, and pepper, and toss well to coat. Place the shrimp on metal skewers or on a grill sheet. Once grill is ready, grill for 2 to 3 minutes on each side or until shrimp are pink and opaque.
Place the orzo in the bowl with the prepared dill dressing and toss to combine. Divide onto plates and top evenly with shrimp. Sprinkle with feta and serve with lemon wedges.