In a small saucepan, combine the mirin, sake and sugar and bring to a simmer on the grill. Whisk until smooth and the sugar is dissolved. Remove from the grill and whisk in the miso, sriracha and rice vinegar. Cool.
Place the cod fillets into a zip-top bag. When the miso mixture has cooled, pour over the cod, seal the bag and marinate in the refrigerator for 1 to 3 days. The longer fish marinates, the better.
Set up your grill for indirect heat. If using a charcoal grill, build the coals on one side only. If using a gas grill, heat one side only. Allow the temperature to reach 400 to 450°F.
Liberally grease the grates of your grill with the oil.
Remove the fish from the marinade and allow the excess to drain off.
Meanwhile, place the limes, cut-side down, onto the direct heat side of the grill and grill until charred, 3 to 4 minutes. Remove from the grill and set aside.
Place the fish, skin-side down, on the indirect heat side of the grill. Cover the grill and cook until the fish is flaky and cooked through, 8 to 10 minutes.
Transfer the fish to a serving platter and squeeze 1 of the grilled limes all over the fish. Serve with the remaining grilled limes.