In a large frying pan, melt 2 tablespoons of the butter in 1 tablespoon of the oil over medium-high heat. Add chicken and shrimp. Sprinkle with oregano, salt, black pepper and cayenne. Saute about 3 minutes, until chicken turns opaque and shrimp turns pink. Remove and set aside.
Reduce heat to medium and add remaining 2 tablespoons butter and 1 tablespoon oil. Add onion and saute until softened, about 3 minutes. Add green pepper and garlic and cook until pepper is crisp-tender, 3 to 5 minutes. Add tomato, Worcestershire sauce, and lemon juice.
Return shrimp and chicken to pan, mix well, and simmer for 5 minutes. Serve over linguine.