Walk the labyrinth

Snails, 34 bytes

A^
\1r|\xud|\Xaa7},(\*|\xud=\x)r},

Expanded:

{
    {
        \1 r |
        \x ud |
        \X aa7
    },
    (\* | \x ud =\x)
    r
},

For a path that takes N steps, the program finds one successful match for each traversal of 0 steps, 1 steps, ..., N - 1 steps.

Haskell, 68 66 65 bytes

(a:b)#l@(c:d)|a<'+'=1+b#d|a>'w'=l#('*':b)|a>'W'=d#b|1<2=b#d
_#_=1

Function # takes both lines as separate parameters. Usage example: "1x1x" # "***X" -> 3.

We just have to count the stars * we step on plus 1 for leaving.

(a:b)#l@(c:d)             -- bind: a -> first char of first line
                                   b -> rest of first line
                                   l -> whole second line
                                   c -> first char of second line (never used)
                                   d -> rest of second line
   |a < '+' = 1+b#d       -- stepped on a *, so add 1 and go on
   |a > 'w' = l#('*':b)   -- x switches lines and replaces the x with *
   |a > 'W' = d#b         -- X switch lines and go on
   |1<2     = b#d         -- the rest (-> 1) simply walks forward
_#_=1                     -- base case: the empty string counts 1 for leaving

Edit: @feersum saved a byte. Thanks!

JavaScript (ES6), 119

l=>{z=-~l.search`
`,l=[...l+' '];for(n=p=0;(c=l[p%=2*z])>' ';p+=c>'X'?z:c>'1'?z+1:c>'0'?1:(++n,1))l[p]='*';return-~n}

Less golfed

l=>{
  z=1+l.search`\n`;
  l=[...l+' '];
  for( n = p = 0; 
       (c=l[p%=2*z])>' '; 
       p += c>'X' ? z : c>'1' ? z+1 : c>'0'? 1 : (++n,1) )
    l[p] = '*';
  return 1+n
}

Test

f=l=>{z=-~l.search`
`,l=[...l+' '];for(n=p=0;(c=l[p%=2*z])>' ';p+=c>'X'?z:c>'1'?z+1:c>'0'?1:(++n,1))l[p]='*';return-~n}

[['x\n*',2]
,['xX*\nx1*',3]
,['*1*\nxxx',3]
,['*X*1*x\nx*1xx*',4]
,['1x1x\n***X',3]
,['1*x1xxx1*x\nx*x1*11X1x',6]
,['xXXXxxx111*\n**xxx11*xxx',6]
].forEach(t=>{
  var i=t[0],k=t[1],r=f(i) 
  console.log('Test result '+r+(r==k?' OK ':' KO (expected '+k+')')+'\n'+i)
})