Old English weall "rampart" (natural as well as man-made), also "defensive fortification around a city, side of a building, interior partition," an Anglo-Frisian and Saxon borrowing (cf. 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." Swedish vall, Danish val are from Low German.
In this case, English uses one word where many languages have two, e.g. 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" (cf. the distinction, not always rigorously kept, in Italian muro/parete, Irish mur/fraig, Lithuanian muras/siena, etc.).
Phrase up the wall "angry, crazy" is from 1951; off the wall "unorthodox, unconventional" is recorded from 1966, American English student slang. Wall-to-wall (adj.) recorded 1953, of carpeting; metaphoric use (usually disparaging) is from 1967.