Prepare the marinade by combining olive oil, lemon juice, garlic, oregano, salt, and pepper.
Place the swordfish steaks in a resealable plastic bag or shallow dish and pour the marinade over them.
Preheat your grill to medium-high heat (around 400°F / 200°C).
Remove the swordfish from the marinade and allow excess to drip off; discard the remaining marinade.
Season the swordfish steaks with additional salt and pepper if desired, then place them on the preheated grill.
Grill the swordfish for 4-5 minutes on each side, or until the fish is opaque and flakes easily with a fork.
Once cooked, remove the swordfish from the grill and let it rest for a few minutes before serving.
Serve the grilled swordfish with lemon wedges on the side.