"a large waterfowl proverbially noted, I know not why, for foolishness" [Johnson], Old English gos "a goose," from Proto-Germanic *gans- "goose" (source also of Old Frisian gos, Old Norse gas, Old High German gans, German Gans "goose"), from PIE *ghans- (source also of Sanskrit hamsah (masc.), hansi (fem.), "goose, swan;" Greek khen; Latin anser; Polish gęś "goose;" Lithuanian žąsis "goose;" Old Irish geiss "swan"), probably imitative of its honking.

Geese are technically distinguished from swans and from ducks by the combination of feathered lores, reticulate tarsi, stout bill high at the base, and simple hind toe. [Century Dictionary]

Spanish ganso "goose" is from a Germanic source. Loss of "n" sound before "s" is normal in English (compare tooth). Plural form geese is an example of i-mutation. Meaning "simpleton, silly or foolish person" is from early 15c. To cook (one's) goose is attested by 1845, of unknown origin; attempts to connect it to Swedish history and Greek fables are unconvincing. Goose-egg "zero" is attested by 1866 in baseball slang, from being large and round. The goose that lays golden eggs (15c.) is from Aesop.

c. 1300, hauk, earlier havek (c. 1200), from Old English hafoc (West Saxon), heafuc (Mercian), heafoc, "hawk," from Proto-Germanic *habukaz (source also of Old Norse haukr, Old Saxon habuc, Middle Dutch havik, Old High German habuh, German Habicht "hawk"), from PIE root *kap- "to grasp" (source also of Russian kobec "a kind of falcon"). Transferred sense of "militarist" attested from 1956, probably based on its opposite, dove.