Add oil to a skillet; heat over medium. Cube chicken and season with salt and pepper; add to skillet. Stirring occasionally, cook 6-8 minutes or until no longer pink inside; set aside to cool.
While chicken is cooking, chop broccoli and cauliflower into smaller florets. Peel and dice carrots, dice apples and onion, and add all to a large mixing bowl along with cashews and cranberries.
In a small bowl mix together the mayo, yogurt, sour cream, lemon juice, and sugar. Add yogurt mixture to veggies and toss to coat evenly.
Add cooled chicken to veggie mixture and stir to coat evenly. Serve immediately or cover and chill for later.