sleeve has 1 distinct synonym spread across 1 of its 2 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 part of a garment that is attached at the armhole and that provides a cloth covering for the arm
small case into which an object fits
Synonyms, antonyms and the broader and narrower relations for sleeve come from Princeton University’s WordNet. Full sources and licences.