Cut licorice into shapes to resemble the eyes, nostrils and mouths for 12 alien heads; set aside. Place popcorn in a large greased bowl; set aside. In a small bowl, combine the water, baking soda, vanilla and green food coloring; set aside.
In a heavy saucepan, combine corn syrup and butter; cook over medium heat until butter is melted. Add sugar; cook and stir until sugar is dissolved and mixture comes to a boil. Cook without stirring until a candy thermometer reads 235° (soft-ball stage), about 2 minutes.
Remove from the heat. Stir in reserved vanilla mixture (mixture will foam). Immediately pour over popcorn, stirring to coat evenly. Cool for about 5 minutes, stirring several times. When cool enough to handle, firmly shape with buttered hands into 4-in.-long teardrop shapes; place on waxed paper.
For icing, combine the confectioners' sugar, water, corn syrup and food coloring until smooth. Place icing in a resealable plastic bag; cut a small hole in a corner of bag. Pipe icing onto popcorn heads to attach alien eyes, nostrils and mouth. Let stand until dry; wrap in plastic.