“Storks,” like the most famous folkloric image of the titular bird — airborne and carrying a hammocked baby in its beak — is a thing at once cute, ungainly and seemingly lighter than air. Centered on the delivery of a wide-eyed, pink-haired poppet by a wisecracking stork (voice of Andy Samberg) and his human companion, the animated comedy is overstuffed with adorableness (along with a bit too much plot).