Cut the cheese into triangles that are a little more than 1/2-inch-thick. Put the flour on a large plate.
Pour olive oil about 1/4-inch deep in a medium skillet. Heat the oil over medium-high heat until very hot, but not smoking.
Dredge the cheese in the flour on both sides and fry, turning once, until golden brown on both sides and soft in the center, about 2 minutes per side for halloumi or 1 minute per side for a creamier feta. Drain on paper towels.
Serve the cheese hot, sprinkled with the oregano leaves and with lemon wedges on the side.