It's got to be Homo sapiens surely. When you look at all other animals on this planet, we are undoubtedly the oddest in terms of behaviour. We wear clothes, cook food, believe in Gods, ride around in metal boxes and live in artifical caves. We have sex in private and we communicate through art. I remember watching a cheesy film called 'The Mating Habits of the Earthbound human.' I think Carmen Electra played the woman in it. It's really quite funny and highlights just how unusual we are.
I have always thought the African Lungfish to be one of the most unusual after seeing a National Geographic feature on them years ago. They live in water until evaporation from harsh climate takes it toll, then they secrete a slime which dries to a protective moisture sealant exposing only the mouth which can then breathe air from primitive lungs until water again becomes plentiful. Lungfish also have feet-like fins that allow them to "walk" back to water in the rain. They can survive in encapsulation for 2-4 years.