Combine olive oil, lemon zest and juice, oregano, sea salt, pepper, paprika, and garlic powder in a medium bowl. Stir to combine. Add shrimp, cover, and transfer to the fridge to marinate for 15-30 minutes.
While shrimp is marinating, cook orzo in a large pot of well-salted water, according to package directions for al dente pasta. Drain and set aside briefly to cool.
To make the dressing, combine lemon juice, olive oil, 1/2 teaspoon oregano, table salt, and pepper in a small jar or liquid measuring cup. Shake or whisk to combine.
Combine cooked orzo, tomatoes, olives, spinach, feta, red onion, and parsley in a large bowl. Drizzle with dressing and toss to combine.
When ready to grill, thread shrimp onto skewers and cook over medium heat for 2-3 minutes on each side, just until pink and opaque. Shrimp cook very quickly, so keep a close eye and remove as soon as they’re done. Serve skewers with orzo salad on the side.