WordNet sense 1 (an overwhelming number or amount):

flood, inundation, torrent

WordNet sense 2 (a heavy rain):

cloudburst, downpour, waterspout, pelter, soaker

WordNet sense 3 (the rising of a body of water and its overflowing onto normally dry land):

alluvion

WordNet sense 4 (fill quickly beyond capacity; as with a liquid):

inundate, swamp

WordNet sense 5 (charge someone with too many tasks):

overwhelm, flood out

WordNet sense 6 (fill or cover completely, usually with water):

submerge