Preheat a grill or grill pan to medium-high. Lay 8 wooden skewers in a baking dish and cover with cold water; soak for 15 minutes (you can skip this step if using metal skewers).
Thread 4 shrimp onto two skewers for each serving. Season the shrimp with the dried oregano and some salt and pepper and drizzle with 1 tablespoon of vegetable oil. Grill the shrimp, turning occasionally, until pink in color and cooked through, about 5 minutes total.
While the shrimp are on the grill, in a medium bowl toss together the tomatoes, cucumbers, olives, olive oil, juice of half the lemon, and some salt and pepper. Let the salad marinate for 5 minutes. Cut the remaining lemon half into wedges
Once the shrimp come off the grill, brush both sides of the bread cheese slices with the remaining vegetable oil and grill just until softened, about 20 seconds per side.
Serve the bread cheese while still warm with the vegetable salad, grilled shrimp, wedges of lemon, and a few drizzles of extra-virgin olive oil.
NotesCook's Note: If your market or local cheese shop doesn't have bread cheese, you can easily use a block of haloumi to make this meal. Taste it before using any salt, though, as haloumi is brined and can vary in its saltiness from brand to brand.