Place each slice of swordfish between 2 sheets of lightly oiled parchment paper or plastic wrap, and pound very gently to uniform thinness. Each slice should be about 5 inches long and 3 inches wide. Trim as necessary. Any odd fragments of swordfish can be incorporated into the filling. Peel off the top sheet of parchment or plastic and sprinkle the fish with salt. Refrigerate until needed.
To make the filling, first make bread crumbs: Preheat the oven to 350°F. Pulse the bread cubes in a food processor until you have fine crumbs. Spread the crumbs on a baking sheet. Drizzle evenly with 3 tablespoons of the olive oil and season with salt and pepper. Toss well to coat. Bake, stirring occasionally, until golden, about 20 minutes. Remove from the oven and measure out ⅔ cup of the crumbs. Reserve any leftover crumbs for another use. Raise the oven temperature to 400°F.
To make the filling, heat 4 tablespoons of the olive oil in a small sauté pan and cook the onion (and any fish remnants) until soft, about 10 minutes. Stir in the ⅔ cup bread crumbs, anchovy (if using), currants, pine nuts, parsley, and half each of the lemon juice and orange juice. Season with salt and pepper, remove from the heat, and let cool.
Oil a 9-by-12-inch baking dish. Place a heaping tablespoon of filling on each swordfish slice and roll up. Secure with a toothpick or kitchen string. Arrange the swordfish rolls side by side in the baking dish, interspersing the bay leaves between the rolls. Sprinkle with the oregano. Drizzle with the remaining 2 tablespoons olive oil and the remaining lemon and orange juices.
Bake until the fish is cooked through, 12 to 15 minutes. While the swordfish rolls are baking, make the sauce: Combine the oregano and garlic in a mortar. Grind with a pestle and gradually add the virgin olive oil to make a paste. Add the lemon juice, salt, pepper, and parsley and mix well. Gradually beat in the mild olive oil. (You can also make this sauce in a blender.) Transfer the swordfish rolls to a platter and serve warm or at room temperature drizzled with the sauce.