Cooking pasta according to instructions on package. Drain and rinse with cold water; set aside in a large bowl. Add surimi, cucumber and green onion; stir into pasta.
Whisk together the canola oil, soy sauce, rice vinegar, ginger, sesame seeds and sesame oil. Gently pour dressing over pasta salad and toss to coat.
Transfer to a large serving platter. Garnish with avocado and grilled nori before serving.