Combine the lemon juice, garlic and 2 tablespoons salt in a blender and blend on low until smooth. Transfer 2 tablespoons of the mixture to a medium bowl and reserve for the yogurt sauce. To the remaining garlic-lemon mixture still in the blender, add the olive oil, wine, mint and oregano and blend until evenly combined. Pour the marinade into a large bowl and add the chicken wings. Sprinkle with some pepper and toss to coat evenly, then cover with plastic wrap and refrigerate for at least 1 hour or up to overnight.
Meanwhile, make the yogurt sauce: Add the yogurt and dill to the bowl containing the reserved garlic-lemon mixture, season with pepper and stir until smooth. Transfer the sauce to a serving bowl, cover with plastic wrap and refrigerate until ready to serve.
Preheat a grill to medium heat. Lightly brush the grill grates with vegetable oil, then grill the chicken wings, turning often to prevent burning, until golden brown, lightly charred at the edges and cooked through, about 25 minutes.
Transfer the wings to a serving platter and season with salt. Drizzle with yogurt sauce and sprinkle with crumbled feta. Serve immediately with lemon wedges on the side.