march has 18 distinct synonyms spread across 9 of its 14 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 act of marching; walking with regular steps (especially in a procession of some kind)
“it was a long march”
a steady advance
“the march of science”
a procession of people walking together
“the march went up Fifth Avenue”
district consisting of the area on either side of a border or boundary of a country or an area
“the Welsh marches between England and Wales”
genre of music written for marching
“Sousa wrote the best marches”
a degree granted for the successful completion of advanced study of architecture
march in protest; take part in a demonstration
“Thousands demonstrated against globalization during the meeting of the most powerful economic nations in Seattle”
cause to march or go at a marching pace
“They marched the mules into the desert”
Synonyms, antonyms and the broader and narrower relations for march come from Princeton University’s WordNet. Full sources and licences.