Preheat oven to 450 degrees with racks in middle and bottom positions. On a rimmed baking sheet, lightly brush corn tortillas on both sides with 2 teaspoons olive oil. Bake on middle rack until golden and crisp, flipping halfway through, 10 to 12 minutes. On a separate rimmed baking sheet, toss sweet potatoes with 2 tablespoons oil. Season with salt and pepper and sprinkle with chili powder. Roast on bottom rack until tender and golden, flipping halfway through, about 30 minutes.
Meanwhile, in a small saucepot, heat remaining teaspoon of oil over medium. Add garlic and cook until fragrant, about 1 minute. Add beans and 1/2 cup water, bring to a simmer and cook until liquid is reduced by half, about 3 minutes. Remove from heat and lightly mash beans with a fork. Spread beans on tostadas, top with sweet potato, jalapenos, onion, and avocado. Serve with lime wedges.