galley (n.)youdaoicibaDictYouDict
13c., "seagoing vessel having both sails and oars," from Old French galie, galee "boat, warship, galley," from Medieval Latin galea or Catalan galea, from Late Greek galea, of unknown origin. The word has made its way into most Western European languages. Originally "low, flat-built seagoing vessel of one deck," once a common type in the Mediterranean. Meaning "cooking range or cooking room on a ship" dates from 1750.

The printing sense of galley, "oblong tray that holds the type once set," is from 1650s, from French galée in the same sense, in reference to the shape of the tray. As a short form of galley-proof it is attested from 1890.
galleywest (adv.)youdaoicibaDictYouDict
indicating where something or someone is knocked, "into an extremely distressed or disabled condition," American English slang, by 1835; considered by OED to be a corruption of western England dialectal collyweston, name of a village in Northamptonshire ("Colin's West Farmstead") that somehow came to signify "askew, not right." But Farmer calls it an Americanism and goes in for it as an "indefinite superlative," and DAS also does not consider the obscure English term to be the source. Early nautical references suggest it might simply be what it looks like: a sailor's generic way of indicating something has been thrown pretty far by impact, based on galley in the "ship's cooking room" sense.
"Matter? why d--n my old shoes, Captain Williams, here is one of that bloody Don Dego's shot gone right through the galley-door, and through the side of the big copper, and knocked all the beef and hot water galley-west. ..." [N.Ames, "Old Sailor's Yarns," New York, 1835]