In a food processor, whirl yellow and green onions, garlic, lime juice, vinegar, chiles, allspice, thyme, pepper, salt, and nutmeg into a paste. With motor running, add soy sauce and oil. Put chicken in a deep bowl, add marinade, and turn to coat. Chill, covered, turning occasionally, at least 4 hours or until next day.
About 30 minutes before cooking, remove chicken from refrigerator. Heat a charcoal, gas, or stove-top grill to medium (about 375°). Lift chicken from marinade and grill, turning every 5 minutes, until well browned and cooked through, about 35 minutes (20 to 35 for individual pieces). Serve with lime wedges.