drop has 49 distinct synonyms spread across 18 of its 32 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
let fall to the ground
“Don't drop the dishes”
terminate an association with
“drop him from the Republican ticket”
utter with seeming casualness
“drop a hint”
lose (a game)
“The Giants dropped 11 of their first 13”
stop associating with
“They dropped her after she had a child out of wedlock”
take (a drug, especially LSD), by mouth
“She dropped acid when she was a teenager”
omit (a letter or syllable) in speaking or writing
“New Englanders drop their post-vocalic r's”
change from one level to another
“She dropped into army jargon”
fall or sink into a state of exhaustion or death
“shop til you drop”
give birth; used for animals
“The cow dropped her calf this morning”
a sudden sharp decrease in some quantity
“a drop of 57 points on the Dow Jones index”
a steep high face of rock
“he stood on a high cliff overlooking the town”
a predetermined hiding place for the deposit and distribution of illicit goods (such as drugs or stolen property)
a free and rapid descent by the force of gravity
“it was a miracle that he survived the drop from that height”
a curtain that can be lowered and raised onto a stage from the flies; often used as background scenery
a central depository where things can be left or picked up
the act of dropping something
“they expected the drop would be successful”
Synonyms, antonyms and the broader and narrower relations for drop come from Princeton University’s WordNet. Full sources and licences.