Cook the whole wheat pasta in salted boiling water until al dente, then drain and rinse with cold water.
In a separate small bowl, whisk the Greek yogurt, Dijon mustard, lemon juice, garlic powder, and dried oregano until smooth.
Combine the cooled pasta, cubed chicken, cherry tomatoes, cucumber, and red onion in a large mixing bowl.
Add the yogurt dressing to the bowl and toss all ingredients until the pasta and vegetables are thoroughly coated.
Gently fold in the crumbled feta cheese and season with salt and pepper.
Serve immediately or refrigerate for 30 minutes to allow flavors to meld.