In a small bowl, mix rice vinegar, sugar, and salt until dissolved. Gently fold this mixture into the cooked sushi rice. Let the rice cool completely.
In another bowl, combine the chopped imitation crab meat, avocado, cucumber, mayonnaise, soy sauce, and wasabi paste (if using).
With wet hands, take a small amount of the seasoned rice and flatten it into a disc. Place a spoonful of the crab mixture in the center and fold the rice around it, forming a ball. Repeat with the remaining rice and filling.
Roll each rice ball in the beaten eggs, then coat with panko breadcrumbs.
Heat vegetable oil in a deep fryer or large pot to 350°F (175°C). Fry the rice balls in batches until golden brown and crispy, about 2-3 minutes per side. Drain on paper towels.
Serve the rice balls with soy sauce, pickled ginger, and wasabi on the side.
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