moving has no recorded synonym. 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. Its 3 recorded opposites are nonmoving, unmoving, still.
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.
arousing or capable of arousing deep emotion
“she laid her case of destitution before him in a very moving letter”
used of a series of photographs presented so as to create the illusion of motion
“Her ambition was to be in moving pictures or `the movies'”
Synonyms, antonyms and the broader and narrower relations for moving come from Princeton University’s WordNet. Full sources and licences.