Heat the oven to 375°F. Put the chicken wings in a large roasting pan, drizzle with the oil, and sprinkle liberally with salt and pepper. Toss to coat and spread the wings out in a single layer.
Roast, undisturbed, until the bottom of the pan is coated with fat and the wings are beginning to brown, about 15 minutes. Use a spoon to baste the wings with the drippings, then carefully pour the extra fat out of the pan and flip them over (if they're sticking give them an extra 5 minutes).
Toss the wings in a combination of 1/4 cup olive oil, 2 to 3 Tbs. freshly squeezed lime juice, 2 Tbs. chili powder, and 1 Tbs. smoked paprika.
Return wings to the oven until both sides are nicely browned, another 10 minutes or so (they'll release easily from the pan when ready).
Raise the oven temperature to 450°F and continue to cook until wings are crisp all over, about 10 minutes. Serve hot, warm, or at room temperature with carrot and celery sticks on the side.