shake has 23 distinct synonyms spread across 12 of its 15 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.
undermine or cause to waver
“my faith has been shaken”
get rid of
“I couldn't shake the car that was following me”
bring to a specified condition by or as if by shaking
“He was shaken from his dreams”
shake (a body part) to communicate a greeting, feeling, or cognitive state
“shake one's head”
grasping and shaking a person's hand (as to acknowledge an introduction or to agree on a contract)
Synonyms, antonyms and the broader and narrower relations for shake come from Princeton University’s WordNet. Full sources and licences.