Extreme homonyms
While not antonymic, several have unrelated meanings.
Note: Several of these words, while spelled the same, differentiate meaning by having different pronunciations.
homonyms but not homophones
Tear - The liquid that flows out of a sad eye or a rip or breach in something, especially cloth.
Lead - The metal which alchymists attempted to turn into gold or the action of offering direction, or the person who performs that function, if used as a noun as in "This teller is the lead."
Wound - An injury to a person or animal or the action of turning or winding something in the past (he wound the watch.)
Wind The movement of air or the action of turning or winding something.
homonyms and homophones
Groom - a man about to be married or the person who cares for horses.
Lie - To deceive by telling an untruth or to rest one's body horizontally such that it is not supported by the feet.
Duck a quacking bird which waddles on webbed feet or the action of bending one's self (duck your head.)
box a cuboid container or a martial sport of fisticuffs.
One of my favourite incongruous pairings is cleave (to split) and cleave (to stick together).
I can literally only think of one (or two):
Literally - used to emphasize the truth and accuracy of a statement or description that is actually true - Factual.
Literally - used in an exaggerated way to emphasize a statement or description that is not actually true (or possible) - Figurative.
First example: I got into a cab and the driver took it literally when asked to go straight across the traffic circle.
Second example: Of course, we got into a wreck! From that moment on, our worlds have literally been turned upside down.
This wasn't always possible until a few years ago when the figurative meaning of the word was added to the dictionary - due to its overuse (and misuse).
According to the dictionary, “literally” now also means “figuratively”