In a medium bowl, whisk oil, chili powder, garlic powder, cumin, 1 tablespoon lime juice, and 1 ½ teaspoons salt.
Arrange mushrooms in a single layer in a shallow glass baking dish. Pour marinade over mushrooms, gently turning to coat as needed. Set aside at room temperature for 30 minutes.
Meanwhile, in a medium bowl, toss cabbage, onion, 2 tablespoons cilantro, and remaining 2 tablespoons lime juice; season with remaining ½ teaspoon salt.
Prepare a grill for medium-high heat; preheat 5 minutes (or heat a grill pan over medium-high heat). Clean and oil grates.
Remove mushrooms from marinade, letting excess drip off. Grill in a single layer, turning halfway through, until deeply marked on both sides, 1 to 2 minutes per side.
Arrange 2 slices avocado and a handful of slaw in the center of each tortilla. Top with 3 to 4 grilled portobello slices and a smattering of cilantro and cotija.