Mix flour, salt, pepper, and oregano together in a shallow dish or bowl. Coat chicken pieces in flour mixture, shaking off excess.
Melt butter over medium heat in a large skillet; pan-fry chicken in butter until lightly brown, 3 to 4 minutes. Turn over chicken and add mushrooms. Pour Marsala wine, red wine, and sherry into the skillet. Cover skillet and simmer, turning once, until chicken is no longer pink and juices run clear, about 10 minutes.