In a small food processor fitted with a metal blade, combine the garlic, salt, and oregano and process until they are minced. With the machine running, slowly pour in the olive oil. Process until it is well blended.
Reserve 2 tablespoons of the marinade for basting. In a large bowl toss the shrimp the remaining marinade.
Oil the grill grate. Remove the shrimp from the marinade and arrange them directly over the fire. Grill for about 5-7 minutes turning once. (I just put them in a big grill basket and kind of tossed them around - I wasn't going to risk having one fall through the grate). Baste the shrimp with the reserved marinade as they grill. Transfer to serving bowl.