Preheat a grill to medium. Microwave the sweet potatoes until soft, 7 to 9 minutes. Let cool slightly, then brush with 1 teaspoon olive oil; season with salt and pepper. Meanwhile, toss the chicken with 1 tablespoon olive oil, the chile powder, cumin and a big pinch each of salt and pepper.
Make the salsa: Combine the strawberries, bell pepper, jalapeno and half each of the scallions and cilantro in a medium bowl. Add the lime juice and season with salt and pepper. Toss well and set aside until juicy.
Oil the grill grates and add the sweet potatoes and chicken. Grill, covered, turning, until the sweet potatoes are tender and charred and the chicken is cooked through, 15 minutes for the sweet potatoes and 16 to 20 minutes for the chicken.
Split open the sweet potatoes. Drizzle with the remaining 2 teaspoons olive oil, sprinkle with the remaining scallions and cilantro and season with salt and pepper; fluff with a fork. Serve the chicken with the sweet potatoes; top the chicken with the strawberry salsa and serve with lime wedges.