Soak bamboo skewers (6" long) in water for 30 minutes. (helps to prevent burning)
Mix soy sauce, sugar, Sake, and Mirin in a small pot, and boil for 8-10 minutes until the sauce gets a little thick. Set aside.
Cut chicken thighs into 1" cubes. Skewer 4-5 chicken pieces onto a soaked bamboo skewer. Roll up sliced pork and skewer 3-4 pieces. Remove stems and cut peppers in half if too long, and skewer 3-4 pieces. Cut Shiitake into halves and skewer 3 pieces diagonally. Cut Naganegi into 2" long and skewer.
On the heated barbecue grill, cook skewered meat at medium heat for 7-8 minutes. Turn and cook another 7-8 minutes until browned and cooked through. Immediately dip meat in the sauce, and serve. Cook vegetables for less time, but until lightly browned, turning a few times. Dip in the sauce or serve with lemon and salt.