"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 first attested 1845, of unknown origin; attempts to connect it to Swedish history and Greek fables are unconvincing. Goose-egg "zero" first attested 1866 in baseball slang, from being large and round. The goose that lays golden eggs (15c.) is from Aesop.
"jab in the rear," c. 1880, from goose (n.), possibly from resemblance of the upturned thumb to a goose's beak, or from the notion of creating nervous excitement. Related: Goosed; goosing. In 19c. theatrical slang, to be goosed meant "to be hissed" (by 1818). A broad range of sexual slang senses historically cluster around goose and gooseberry; goose and duck was rhyming slang for "fuck;" Farmer identifies Winchester goose as "a woman; whence, by implication, the sexual favor," and goose as a verb "to go wenching, to womanize, also to possess a woman." He also has goose-grease for a woman's sexual juices, while gooser and goose's neck meant "the penis." Gooseberries (they are hairy) was "testicles," and gooseberry pudding "a woman."