#JavaScript (ES6) 340 372 446
Not counting indentation white space and newlines - could be golfed more.
Using an '*' to mark new lines in input, as prompt accepts a single line.
F=s=>[0,13,26].map(r=>
o+=[...s].map(c=>
' \\1/ \\ /1\\ / V ^ 1><1 --++-++-- 1||1||1 '.substr(
(c=c.charCodeAt()-(c>'`'?97:65))<0
?0
:c<18
?27+3*a[f=9,c%9+r+4]
:c<26
?3*a[f=22,c%4+r]
:0,3)
.replace(1,13-r||c<f?' ':'.')
).join(' ')+'\n',o='',
a='460234501201283173453453452054012012345'
)&&o;
console.log(prompt().split('*').map(s=>F(s)).join('\n'))
Test in FireFox/FireBug console
Input: ABCDEFGHIJKLMNOPQRSTUVWXYZHeLlO WoRlD!
| | | | --+ +-+ +-- --+ +-+ +--
| | | | | | | | | | | |
--+ +-+ +-- --+ +-+ +-- | | | |
| | | | --+ +-+ +-- --+ +-+ +--
.| |.| |. .| |.| |. .| |.| |.
--+ +-+ +-- --+ +-+ +-- | | | |
\ / ^
\ / > < / \
V / \
\ / ^
\./ .> <. /.\
V / \
+-+ +-+ | | +-- +-- +-- | --+
| | | | |. |. |. \./ |. |. |. |
| | +-+ +-- +-- +-- V +-- | +-- --+