In microwavable bowl, combine vinegar, sugar and salt. Microwave on high for 30 seconds; stir and heat at heat at 15-second intervals, if necessary, until warmed through and sugar dissolves.
Spread cooked rice onto rimmed baking sheet in single layer. Drizzle vinegar mixture evenly over rice; fold in gently until rice is coated. Let cool to room temperature.
Slice avocado into 1/4-inch (5 mm) thick slices. Slice crab sticks in half lengthwise.
Place plastic wrap over bamboo rolling mat. Place nori, shiny side down, on plastic wrap. Lay one-quarter of the rice mixture evenly onto nori; using wet fingers, spread to edges, leaving 1-inch (2.5 cm) border on far edge. Place two avocado slices and 2 pieces crab along close edge.
Holding filling in place with fingers, tightly roll up mat over filling into tight cylinder. Pull mat and plastic away. Cover sushi roll with damp towel and repeat with remaining nori and filling. Cut each roll into 6 pieces.