X Marks the Spot

Python 3, 577 519 515 490 475 467 454 bytes

def c(g,d):
 R,L,V,e,b=range,list,len,'-|+','#';t,g=(lambda g,d:sum([[(i,j)for j in R(V(L(g.split('\n')[i])))if g.split('\n')[i][j]==d]for i in R(V(g.split('\n')))],[]))(g,d),[L(i)for i in g.split('\n')]
 for a,r in t:
  for j in R(a-3,a+4):
   if V(g)>j>-1:n=g[j][r];g[j][r]='+'if n in e else'#'if n in(d,b)else'|'
  for j in R(r-5,r+6):
   if V(g[a])>j>-1:n=g[a][j];g[a][j]='+'if n in e else'#'if n in(d,b)else'-'
 return'\n'.join(''.join(l)for l in g)

I'm not sure how much farther I can golf this.

Usage:

c(g, d)

Where g is the input grid and d is the crosshair-marking character.

Perl, 370 bytes

sub r{$h=pop;($=[$n=pop].=$"x(1+"@_"-length$=[$n]))=~s!(.{@_})(.)!"$1".($2=~/[-|+]/?'+':$2=~/[X#]/?'#':$h)!e}map{chop;push@c,[$-,pos]while/X/g;$-++}@==<>;($x,$y)=@$_,3-$x>$a?$a=3-$x:0,$x+5-@=>$b?$b=$x+5-@=:0,6-$y>$c?$c=6-$y:0 for@c;@==($",@=)for 1..$a;$_=$"x$c.$_ for@=;map{($x,$y)=@$_;$_&&r$y+$c+$_-1,$x+$a,'-'for-5..5;$_&&r$y+$c-1,$x+$_+$a,'|'for-3..3}@c;print@=,$,=$/

Usage, save above as xmarks.pl:

perl xmarks.pl <<< 'X'

I'm not sure how much smaller I can make this, but I'm sure I'll come back to it later! I might post an explanation if anyone is interested too.

Handles input of X and non-square inputs as well now.

CoffeeScript, 345 336  327 bytes

Z=(s,c)->s in'X#'&&'#'||s in'-|+'&&'+'||c
X=(s)->l=u=0;o=(r.split ''for r in s.split '\n');c in'X#'&&(i-x&&(o[y][i]=Z o[y][i],'-';i<l&&l=i)for i in[x-5..x+5];i-y&&((o[i]?=[])[x]=Z o[i][x],'|';i<u&&u=i)for i in[y-3..y+3])for c,x in r for r,y in o;((o[y][x]||' 'for x in[l...o[y].length]).join ''for y in[u...o.length]).join '\n'

X is the function to call.

Explained:

# get new char. s - old char. c - '|' or '-'
Z=(s,c)->s in'X#'&&'#'||s in'-|+'&&'+'||c

X=(s)->

  # leftmost and upmost positions
  l=u=0

  # split input into 2D array
  o=(r.split ''for r in s.split '\n')

  # for every 'X' or '#'
  c in'X#'&&(

    # for positions to left and right
    i-x&&(

        # draw horisontal line
      o[y][i]=Z o[y][i],'-'

      # update leftmost position
      i<l&&l=i

    )for i in[x-5..x+5]

    # for positions above and below
    i-y&&(

      # add row if necessary and draw vertical line
      (o[i]?=[])[x]=Z o[i][x],'|'

      # update upmost position
      i<u&&u=i

    )for i in[y-3..y+3]

  )for c,x in r for r,y in o

  # concatenate into string, replacing empty chars with spaces
  ((o[y][x]||' 'for x in[l...o[y].length]).join ''for y in[u...o.length]).join '\n'

Executable:

<script src="http://coffeescript.org/extras/coffee-script.js"></script>
<script type="text/coffeescript">

Z=(s,c)->s in'X#'&&'#'||s in'-|+'&&'+'||c
X=(s)->l=u=0;o=(r.split ''for r in s.split '\n');c in'X#'&&(i-x&&(o[y][i]=Z o[y][i],'-';i<l&&l=i)for i in[x-5..x+5];i-y&&((o[i]?=[])[x]=Z o[i][x],'|';i<u&&u=i)for i in[y-3..y+3])for c,x in r for r,y in o;((o[y][x]||' 'for x in[l...o[y].length]).join ''for y in[u...o.length]).join '\n'

################################################################################
# tests follow
s = ['''
                mdhyyyyyyyhhhddmmm                
            mdyyssoo  oooosyyyhhhdmm              
          hsso     oossoooooyyhhdhhdmmm           
        yoooooo     oo ssysssyhhdyyyhmmmm         
      myso oso  o  oyo    hhhdhhyhyhhm mm m       
     mhsyhhys  oss      yyyhhhsosyhhmmmmdmmm
    mhyhhhy y         ssyhoho o shhdmmmmdmmmm        
    hhyyyh   s   oo syysyyhhdysso oyhdhhhmmmmm     
   dhysyys      sdysoXoyyyyhhso     syshm  mmm    
   hhyhyo       o      osss y   shhyyhd mmmmmm    
   yyhyyyss           o  oyyyydmmdmmmmmmmmm mm    
   ysyhyhhho   s     osy  sdm m  mddmmddhydmmm   
   h  oshhhyyyddhoo  ooyysshdmdohdmmdmddsshmmm    
    y   oyhhhdhhsyhsssshdddsss    hdddyyyhddm     
    dyyshyyhssyyhyyyyddhhmmdmmmdy syssoosyhdm     
     hsyyhhhhsoo sooyyhhdoohdhhyhyysoo  osdm      
      doyhhhyyyyhhhysyyy oossyyssso   osydm       
        soyhyyhhhhhhyhyyyooos       ohdddm        
         msoyyyyyyyhyyyyo ooo       syyd          
            ho oyyysooo    osso   osyd            
               dhyyysssyyyyyysoosdm               
                    mmdddddmmm                    
'''
'''
000000000000
000000000000
0000X0000000
0000000X0000
000000000000
000000000000
000000000000
000000000000
000000000000
000000000000
000000000000
000000000000
'''
'''
00000000000000000
00000000000000000
00000000000000000
00000X000X0000000
00000000000000000
00000000000000000
00000000000000000
00000000000000000
00000000000000000
00000000000000000
00000000000000000
00000000000000000   
'''
'X'
'XX\nXX'
]
document.write '<pre>'
document.write '\n\n',X x for x in s
</script>