Combine first 5 ingredients in electric blender or food processor; cover and process until smooth. Remove giblets and rinse chickens with cold water; pat dry. Place 2 stems of fresh sage, 1 tsp of oregano, and 2 halved garlic cloves in cavity of each chicken.
Tie ends of legs together with kitchen string. Lift wingtips up and over back and tuck under bird. Secure chickesn to rotisserie spit over drip pan surrounded by hot coals. Brush birds with oil mixture. Continue brushing every 5 to 7 minutes, while maintaining an even medium heat. After 30 to 40 minutes, carefully insert meat thermometer into meaty interior portion of a thigh on each chicken.
Chickens are done when temperature reaches 180 degrees. Once done, remove chicken to warmed platter. Untie birds and remove sage and garlic from chicken cavities; reserving garlic cloves. Remove chicken to a serving platter; set aside and keep warm.
Skim fat from pan drippings. Combine drippings with vinegar, sage, reserved garlic cloves, and mustard in electric blender or food processor; blend until smooth. Accompany chicken with sauce.