mouth has 14 distinct synonyms spread across 4 of its 11 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.
the opening through which food is taken in and vocalizations emerge
“he stuffed his mouth with candy”
an opening that resembles a mouth (as of a cave or a gorge)
“he rode into the mouth of the canyon”
the point where a stream issues into a larger body of water
“New York is at the mouth of the Hudson”
a person conceived as a consumer of food
“he has four mouths to feed”
the opening of a jar or bottle
“the jar had a wide mouth”
Synonyms, antonyms and the broader and narrower relations for mouth come from Princeton University’s WordNet. Full sources and licences.