Preheat a grill to medium-high (if you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 3 to 4 seconds). Season tomatoes with salt and pepper; drizzle with about 2 tablespoons oil. Grill tomatoes, cut side down, until marked by grill and beginning to soften, 5 to 7 minutes. Flip tomatoes, and grill until soft and juicy, but still holding shape, 5 to 7 minutes more. Transfer to a cutting board, and coarsely chop. Transfer to a medium bowl. Add oregano, and toss to combine. Season with salt, and drizzle with remaining oil; set aside.
Grill sausages, turning occasionally, until browned and cooked through, about 12 minutes. Cut each sausage in half lengthwise. Using a slotted spoon, divide tomatoes among focaccia; top each with a sausage half, arranging cut side down. Serve immediately.