Place the trimmed chicken wings in a large bowl.
Add the salt and pepper, garlic powder, dried oregano, and olive oil to the bowl.
Toss the wings thoroughly to coat evenly in the spice mixture and oil.
Preheat your grill to medium-high heat. Arrange the wings on the grill in a single layer.
Grill the wings for 25–35 minutes, turning every 5 minutes, until cooked through and crisped; aim for an internal temperature of 170–175°F (77–79°C).
Remove the wings from the grill and divide them evenly into two bowls.
Add the BBQ sauce to one bowl and toss to coat the wings well.
Add the hot sauce to the other bowl and toss to coat those wings evenly.
Arrange the BBQ and hot wings side by side on a large platter and serve with blue cheese dip.
Garnish with lemon wedges, parsley, or extra red chilies if desired.