influence has 8 distinct synonyms spread across 3 of its 8 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.
causing something without any direct or apparent effort
a cognitive factor that tends to have an effect on what you do
“her wishes had a great influence on his thinking”
the effect of one thing (or person) on another
“the influence of mechanical action”
one having power to influence another
“she was the most important influence in my life”
Synonyms, antonyms and the broader and narrower relations for influence come from Princeton University’s WordNet. Full sources and licences.