Preheat the oven. Preheat your oven to 425°F (220°C). Prepare a large sheet pan.
Prepare the vegetables. Cut the potatoes into quarters, slice the red onion, and halve the grape tomatoes. Set the tomatoes aside for later.
Make the seasoning mixture. In a large bowl, whisk together the olive oil, lemon juice, minced garlic, oregano, paprika, garlic powder, onion powder, salt, and black pepper.
Coat the potatoes and onions. Add the potatoes and sliced onions to the bowl. Toss until everything is coated with the olive oil mixture. Transfer the vegetables to the sheet pan using a large spoon, leaving the remaining mixture in the bowl.
Coat the chicken. Add the chicken drumsticks to the same bowl and toss them in the remaining seasoning mixture until well coated.
Arrange and bake. Place the chicken drumsticks on the sheet pan with the potatoes and onions. Bake for 40–45 minutes, or until the chicken reaches an internal temperature of 165°F and the potatoes are fork-tender.
Add the toppings. Remove the pan from the oven and top with the halved grape tomatoes and crumbled feta cheese before serving.