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.
c. 1300, wawil-eghed, wolden-eiged, "having very light-colored eyes," also "having parti-colored eyes," from Old Norse vagl-eygr "having speckled eyes," from vagl "speck in the eye; beam, upper cross-beam, chicken-roost, perch," from Proto-Germanic *walgaz, from PIE *wogh-lo-, suffixed form of root *wegh- "to go, move, transport in a vehicle." The prehistoric sense evolution would be from "weigh" to "lift," to "hold, support." Meaning "having one or both eyes turned out" (and thus showing much white) is first recorded 1580s.