Back at the Barnyard/WMG

Otis is a Transsexualism
Otis is a transsexual cow who was turned into a steer, but they forgot to remove the udders.

Alternately, Otis is a Bifauxnen
And a lesbian, apparently.

The farmer is a Mad Scientist
Otis (and, in The Movie, his "father" Ben) are the results of the farmer's sick, twisted experiments, creating a female cow with a male cow's personality, behaviors, and identity. Additionally, Freddie the "ferret" is actually an abomination created by the farmer by fusing several different species' genetic codes together into an unholy combination that does not even remotely resemble a real ferret in appearance or personality, and is only called such to hide the fact that he's actually the result of a disturbing fusion. Freddie's parents were also created by the farmer as additional cover-up - if they appear to be a family, then it's not nearly as obvious that they were engineered into existence.