offer has 17 distinct synonyms spread across 11 of its 16 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.
put forward for consideration
“He offered his opinion”
produce or introduce on the stage
“The Shakespeare Company is offering `King Lear' this month”
threaten to do something
“I offered to leave the committee if they did not accept my proposal”
Synonyms, antonyms and the broader and narrower relations for offer come from Princeton University’s WordNet. Full sources and licences.