Mix the onion, tomatoes, olives, cucumber, oregano and feta together in a small bowl. Add the lemon juice, season to taste with pepper and gently mix.
Split each pitta bread in half horizontally. Divide the feta mixture between the bottom halves of the pitta breads, then add the Cheddar. Cover with the top halves of the pitta breads.
Brush a griddle pan with oil and heat over a medium heat. When hot, add the sandwiches, press down gently with a spatula and cook for 2–3 minutes on each side until golden and the cheese has melted. Serve immediately.