Clean the fish, removing any scales, gills, and offal, wash them very well, cut into large pieces, and place in a steaming basket. Slice the onions, carrots, and potatoes, into pieces of roughly the same size.
In a large pot, add the water and onions, potatoes, carrots, tomatoes, celery, the stock cube, parsley, and bay leaf.
Place the basket with the fish on top of the water, and add 1/2 cup olive oil. Cover the pot and boil for 30 minutes. Remove the lid, take out the basket with the fish, remove the bones from the fish, and place them on a serving dish.
Drain the soup and reserve the stock. Puree the vegetables and place them back into the stock, and boil them together with the rice for about 20-25 minutes.
Mix the olive oil with the lemon juice, salt, pepper, and oregano, and pour over the fish. Serve the soup in deep bowls.