"animals of the mammalian order Cetacea," Old English hwæl "whale," also "walrus," from Proto-Germanic *hwalaz (source also of Old Saxon hwal, Old Norse hvalr, hvalfiskr, Swedish val, Middle Dutch wal, walvisc, Dutch walvis, Old High German wal, German Wal), from PIE *(s)kwal-o- (source also of Latin squalus "a kind of large sea fish"). In popular use it was applied to any large sea animal. Phrase whale of a "excellent or large example" is c. 1900, student slang. Whale-oil attested from mid-15c.
"pursue the business of whale-fishing," 1700, from whale (n.). Whale-fishing is attested from 1570s.
"beat, whip severely," 1790, possibly a variant of wale (v.) "to mark with 'wales' or stripes" (early 15c.), from wale (n.). Related: Whaled; whaling.