Rinse the sushi rice under cold water until the water runs clear. Drain well. In a medium saucepan, combine the rinsed rice and water. Bring to a boil, then reduce heat to low, cover, and simmer for 18-20 minutes until the rice is tender and water is absorbed. Remove from heat and let it sit, covered, for 10 minutes.
In a small bowl, mix together the rice vinegar, sugar, and salt until dissolved. Gently fold this mixture into the cooked rice, being careful not to mash the grains. Allow the rice to cool to room temperature.
While the rice cools, heat the vegetable oil in a skillet over medium heat. Add the sliced Spam and cook until browned and crispy, about 3-4 minutes on each side. Drizzle with soy sauce and cook for an additional minute. Remove from heat.
Wet your hands with water to prevent sticking. Take a handful of rice (about 1/2 cup) and form it into a triangle or oval shape. Make an indentation in the center and place a slice of Spam and a slice of avocado inside. Mold the rice around the filling to encase it completely.
Wrap a strip of nori around the onigiri, leaving one side open for easy handling. Repeat with the remaining rice, Spam, and avocado.
If desired, sprinkle sesame seeds on top for garnish. Serve immediately or refrigerate for up to 2 hours before serving.