disposal has 4 distinct synonyms spread across 3 of its 4 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.
the power to use something or someone
“used all the resources at his disposal”
a method of tending to or managing the affairs of a some group of people (especially the group's business affairs)
a kitchen appliance for disposing of garbage
Synonyms, antonyms and the broader and narrower relations for disposal come from Princeton University’s WordNet. Full sources and licences.