stalk has 10 distinct synonyms spread across 6 of its 8 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.
a slender or elongated structure that supports a plant or fungus or a plant part or plant organ
a hunt for game carried on by following it stealthily or waiting in ambush
go through (an area) in search of prey
“stalk the woods for deer”
Synonyms, antonyms and the broader and narrower relations for stalk come from Princeton University’s WordNet. Full sources and licences.