In small bowl, whisk together vinegar, mustard, oregano, lemon-pepper and salt. Gradually whisk in oil until dressing is thick and well blended.
Heat oven to 425°F. Coat bottom of large roasting pan with vegetable oil. In large bowl, toss chicken and sausage with 6 tablespoons dressing. Place in roasting pan.
Roast in 425°F oven 15 minutes.
In bowl, toss potatoes, onion and garlic with 3 tablespoons dressing. Arrange in pan with chicken and sausage. Roast another 40 minutes or until potatoes are tender and chicken registers 170°F on instant-read thermometer. Stir ingredients in pan halfway through cooking.
Stir in olives and fresh oregano. Drizzle with remaining dressing. Serve from the roasting pan.