Rinse fish and pat dry. Peel onions and cut lengthwise into quarters, keeping root ends intact. Brush both sides of the fish fillets and the onion quarters with oil. Sprinkle evenly with salt and pepper. Wrap stack of tortillas in foil.
Set tortillas and onions on an oiled barbecue grill over medium-hot coals or medium-high heat on a gas grill (you can hold your hand at grill level only 3 to 4 seconds); close lid on gas grill. Cook tortillas until hot, turning 2 or 3 times, 10 to 15 minutes total. Place warm tortillas in a napkin-lined basket. Cook onions, turning once, until cooked through and lightly charred, 10 to 15 minutes total.
Grill the fish, turning once, until barely opaque in center of thickest part (cut to test), 6 to 8 minutes total.
Arrange fish, onions, and lime wedges on a platter or divide among plates. Offer relish and salsa to add to taste.