Preheat the oven to 325 degrees F. Line a baking sheet with foil and set aside. Heat the vegetable oil and 3 popcorn kernels in a large saucepan over medium heat. When the kernels pop, add the remaining popcorn and cover the pan. Cook, shaking the pan frequently, until the popping has almost stopped, 3 to 5 minutes. Remove from the heat and let stand for a few minutes, covered. Uncover and discard any unpopped kernels.
Transfer the popcorn to a large bowl and add the cereal, sesame sticks and pretzel sandwiches; toss well. Melt the butter in a small saucepan over medium heat; whisk in the garlic powder, mustard powder, sugar, paprika, 1/2 teaspoon salt and a few grinds of pepper. Pour the butter mixture over the snack mix and toss well to coat.
Spread the snack mix in a single layer on the prepared baking sheet. Bake, gently stirring halfway through, until the popcorn is crisp, 15 to 20 minutes. Let cool. Transfer to a large bowl, add the cheese balls and toss to coat.