Skewer neck skin of hens to back; tie legs to tail. Twist wings under back. Place hens, breast up, on a rack in a large shallow roasting pan. Place carrots, parsnips, turnips, and onions around hens in pan. Combine oil, garlic, rosemary, oregano, and salt; brush onto hens and vegetables.
Roast, uncovered, in a 375 degree F oven for 1-1/4 to 1-1/2 hours or until hens are no longer pink and the drumsticks move easily in their sockets.(Internal temperature should be 180 degrees F with an instant-read thermometer.) During roasting, turn vegetables occasionally. Transfer hens from roasting pan to serving platter. Cover and keep warm. Remove rack from roasting pan. Stir vegetables. Increase oven temperature to 450 degrees F. Continue roasting vegetables for 15 to 20 minutes more or until tender and browned.
To serve, using a slotted spoon, spoon vegetables around hens on platter. Makes 4 servings.