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”
Synonyms, antonyms and the broader and narrower relations for wheel come from Princeton University’s WordNet. Full sources and licences.