In a medium bowl, whisk together the oil, garlic, oregano, lemon juice, and zest and season with salt and pepper.

Alternately thread the shrimp, squash, onion, and zucchini onto the skewers, using 4 shrimp per skewer.

Put the kebabs in a shallow baking dish and pour the marinade over the top. Marinate the kebabs at room temperature, turning occasionally, for 10 minutes.

Preheat an indoor grill pan or an outdoor grill. Grill the kebabs, turning and basting with the marinade occasionally, until lightly charred and just-cooked through, about 4 minutes.