Old English weall, Anglian wall "rampart, dike, earthwork" (natural as well as man-made), "dam, cliff, rocky shore," also "defensive fortification around a city, side of a building," an Anglo-Frisian and Saxon borrowing (Old Saxon, Old Frisian, Middle Low German, Middle Dutch wal) from Latin vallum "wall, rampart, row or line of stakes," apparently a collective form of vallus "stake," from PIE *walso- "a post." Swedish vall, Danish val are from Low German.
Meaning "interior partition of a structure" is mid-13c. In this case, English uses one word where many languages have two, such as German Mauer "outer wall of a town, fortress, etc.," used also in reference to the former Berlin Wall, and wand "partition wall within a building" (compare the distinction, not always rigorously kept, in Italian muro/parete, Irish mur/fraig, Lithuanian mūras/siena, etc.). The Latin word for "defensive wall" was murus (see mural).
Anatomical use from late 14c. To give (someone) the wall "allow him or her to walk on the (cleaner) wall side of the pavement" is from 1530s. To turn (one's) face to the wall "prepare to die" is from 1570s. Phrase up the wall "angry, crazy" is from 1951; off the wall "unorthodox, unconventional" is recorded from 1966, American English student slang. To go over the wall "escape" (originally from prison) is from 1933. Wall-to-wall (adj.) recorded 1939, of shelving, etc.; metaphoric use (usually disparaging) is from 1967.
Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."
As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.
1550s, "to drive and catch (swans)," from up (adv.). Intransitive meaning "get up, rise to one's feet" (as in up and leave) is recorded from 1640s. Sense of "to move upward" is recorded from 1737. Meaning "increase" (as in up the price of oil) is attested from 1915. Compare Old English verb uppian "to rise up, swell." Related: Upped; upping. Upping block, used for mounting or dismounting horses, carriages, etc., is attested from 1796 (earlier was horsing-block, 1660s).