F#, 725 chars
open System
let mutable h,s,l=0,Set.empty,Console.ReadLine()
while l<>null do
l.Split([|' '|],StringSplitOptions.RemoveEmptyEntries)
|>Seq.iter(fun t->s<-s.Add(int t,h,(" "+l+" ").IndexOf(" "+t+" ")))
h<-h+1;l<-Console.ReadLine()
let w=Seq.map(fun(k,h,x)->x)s|>Seq.max
let o=Array2D.create h (w+1)' '
Seq.sort s|>Seq.pairwise|>Seq.iter(fun((_,b,a),(_,y,x))->
let a,b,x,y=if b>y then x,y,a,b else a,b,x,y
o.[b,a]<-'+'
o.[y,x]<-'+'
if b=y then for x in(min a x)+1..(max a x)-1 do o.[y,x]<-'-'
elif a=x then for h in b+1..y-1 do o.[h,x]<-'|'
elif a
Legend:
h = height
s = set
l = curLine
w = (one less than) width
o = output array of chars
Lines 1-6: I keep a set of (number, lineNum, xCoord) tuples; as I read in each line of input I find all the numbers and add them to the set.
Line 7-8: Then I create an array of output chars, initialized to all spaces.
Line 9: Sort the set (by 'number'), then take each adjacent pair and ...
Lines 10-16: ... sort so (a,b) is the 'highest' of the two points and (x,y) is the other. Put the '+' signs, and then if horizontal, draw that, else if vertical, draw that, else draw the correct diagonal. If the input is not 'valid', then who knows what happens (this code was littered with 'asserts' before I golf-ized it).
Lines 17-19: Print the result
