Heat the vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Stir in the chili powder. Add the squash, poblano, oregano, cumin, garlic and 1/2 teaspoon salt and cook, stirring frequently, until the poblano softens slightly, about5 minutes. Add 5 cups water, the tomato puree and 1/2 teaspoon salt; cover and bring to a simmer. Uncover and cook until the squash is tender, about 15 minutes, adding the hominy during the last 2 minutes of cooking.
Season the posole with salt and divide among bowls. Top with the avocado and salsa and sprinkle with oregano. Serve with chips.