Liquid drug transfer devices with universal drug vial adapters for use with a drug vial of a small drug vial and a large drug vial. Some universal drug vial adapters employ the same generally opposite upright flex members for clamping a small drug vial and a large drug vial. Other universal drug vial adapters include a set of minor flex members for clamping a small drug vial and a set of major flex members encircling the set of minor flex members for clamping a large drug vial whereupon the large drug vial underlies the set of minor flex members. Liquid drug transfer devices with a universal injection port connector for attachment on an injection port of an infusion bag.