For the chicken: In a medium bowl, whisk together the olive oil, salt, oregano, garlic powder, pepper and lemon juice. Add the chicken and toss to coat. Refrigerate for at least 30 minutes and up to 4 hours.
Preheat a grill or grill pan to medium high.
Remove the chicken from the marinade. Grill the chicken until cooked through, about 5 minutes per side. Slice the chicken into 1-inch-wide pieces. Set aside.
For the breadcrumbs: Preheat the oven to 400 degrees F.
In a medium ovensafe skillet, heat the butter, olive oil and garlic over low heat until the garlic begins to sizzle. Add the breadcrumbs and salt and toss to coat. Transfer to the oven and toast until golden brown, 3 to 4 minutes.
For the dressing: Whisk together the olive oil, vinegar, salt, oregano, pepper, garlic and lemon juice in a small bowl until combined.
For the salad: Bring a large pot of salted water to a boil. Add the orzo and cook until al dente, 7 to 8 minutes. Drain and transfer to a large serving bowl. Toss with the dressing while still hot, then let cool to room temperature.
When cool, stir in the tomatoes, cucumber and parsley. Top with the feta, sliced chicken and breadcrumbs.