Preheat oven to 350 degrees F (175 degrees C).

Heat oil in a very large skillet over medium heat. Add chicken strips; cook and stir until browned, 1 to 2 minutes per side. Transfer to a casserole baking dish.

Place cremini mushrooms, oyster mushrooms, shiitake mushrooms, and garlic in the same skillet; cook and stir until tender, about 5 minutes. Stir in flour until well-incorporated. Slowly mix in white wine. Add chicken stock, sage, salt, and black pepper; bring sauce to a simmer and cook, until thickened, about 5 minutes. Remove from heat and stir in heavy cream.

Pour sauce over chicken in the casserole dish; stir gently to combine. Cover with aluminum foil.

Bake in the preheated oven until bubbly, about 30 minutes. Garnish with parsley before serving.