wheel has 9 distinct synonyms spread across 8 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.
a simple machine consisting of a circular frame with spokes (or a solid disc) that can rotate on a shaft or axle (as in vehicles or other machines)
forces that provide energy and direction
“the wheels of government began to turn”
a circular helm to control the rudder of a vessel
game equipment consisting of a wheel with slots that is used for gambling; the wheel rotates horizontally and players bet on which slot the roulette ball will stop in
an instrument of torture that stretches or disjoints or mutilates victims
a wheeled vehicle that has two wheels and is moved by foot pedals
change directions as if revolving on a pivot
“They wheeled their horses around and left”
wheel somebody or something
Synonyms, antonyms and the broader and narrower relations for wheel come from Princeton University’s WordNet. Full sources and licences.