Preheat the grill to medium-high heat. Brush the swordfish with 2 tablespoons of oil. Grill the fish until done. Set aside and let cool. Chop into bite-sized pieces and place in a square pyrex pan.
Heat 2 tablespoons of oil in a skillet. Add the onion and sauté for two minutes, then add peppers and garlic and continue cooking for about 3 more minutes, stirring occasionally.
Pour in the vinegar and add the seasonings. Cook for 5 more minutes. Adjust salt, as desired. Pour the vinegar/vegetable mixture over the swordfish. Sprinkle capers on top and chill covered, for at least 4 hours.
Divide the greens between four bowls and spoon the swordfish mixture with vinaigrette over the greens. (You may want to adjust the amount of the vinaigrette. The swordfish mixture is well-marinated, so just spooning it over the greens might be enough for you).