To make the marinade: Place olive oil, garlic, oregano, salt and ground pepper in a small bowl. Whisk and leave for later.
Arrange the onion quarters into pieces with two or three layers. Cut the quartered peppers into similar sizes than the onions. Make the souvlaki by threading five pieces of swordfish on to each metal skewer. Alternate the cubes with a piece of onion and and green pepper to add flavour to the fish. Repeat with each kebab.
Lay in a dish and brush the marinade over all the sides of the fish and vegetables and leave for about an hour in a cool place for the flavours to infuse.
Preheat an oiled grill or barbecue to hot setting and place the swordfish kebabs on the grill for cooking. Grill for about 10 minutes, turning to cook on all sides until the fish is cooked through and the onions and peppers are cooked. You can brush the extra marinade over the fish as you are cooking to enhance the flavours.
Serve immediately with the lemon wedges.
*Many fishmongers will prepare and cut the fish for your swordfish recipes. If you are cutting it yourself, you will need about 5 cm square cubes.