Protect my walls from these pesky doors
Scala, 860 bytes

Golfed:

    object D extends App{val s=args(0)split("\n")
    val r=Seq(P(1,0),P(1,-1),P(0,-1),P(-1,-1),P(-1,0),P(-1,1),P(0,1),P(1,1))
    var m=r(0)
    val e=s.map(_.toCharArray)
    case class P(x:Int,y:Int){def u=x==0||h
    def h=y==0
    def p(o:P)=P(x+o.x,y+o.y)
    def o="\\/".contains(c)
    def w="-|+".contains(c)
    def c=try s(y)(x) catch {case _=&gt;'E'}
    def n=r.filter(!_.u).map(d =&gt; d.j(p(d))).sum
    def j(t:P):Int=if(t.o)1+j(p(t))else 0
    def q=if(c=='X'){m=this
    r.filter(_.u).map{d=&gt;if(p(d).c==' '&amp;&amp;p(P(d.x*(n+1),d.y*(n+1))).w)d.i}}
    def i:Unit=Seq(r++r,(r++r).reverse).map(l=&gt;l.drop(l.indexOf(this)+1)).map(_.take(4)).filter(_.exists(a=&gt;a.p(m)o))(0).grouped(2).foreach{p=&gt;if(p(1)p(m)w){p(0)add;return}}
    def add=if(r.filter(_.h).map(p(_)p(m)).exists(_.w))e(y*m.n+m.y)(x+m.x)='.'else e(y+m.y)(x*m.n+m.x)='.'}
    val f=args(0).size
    Array.tabulate(f,f){(i,j)=&gt;P(i,j)q} 
    e.map(_.mkString).map(println)}


Un-golfed:

    object DoorknobCleanVersion extends App {
            val s = args(0) split ("\n")

            val r = Seq(P(1, 0), P(1, -1), P(0, -1), P(-1, -1), P(-1, 0), P(-1, 1), P(0, 1), P(1, 1))
            val HorizontalDirections = r.filter(_.isHorizontal)

            var hinge = r(0)
            val result = s.map(_.toCharArray)

            type I = Int
            case class P(x: Int, y: Int) {
                    def isCardinal = x == 0 || isHorizontal
                    def isHorizontal = y == 0

                    override def toString = x + "," + y

                    def p(o: P) = P(x + o.x, y + o.y)

                    def isDoor = Seq('\\', '/').contains(charAt)
                    def isWall = Seq('-', '|', '+').contains(charAt)

                    def charAt = try s(y)(x) catch { case _ =&gt; 'E' }

                    def doorLength = r.filter(!_.isCardinal).map(d =&gt; d.recursion2(p(d))).sum

                    def recursion2(currentPosition: P): Int =
                            if (currentPosition.isDoor)
                                    1 + recursion2(p(currentPosition))
                            else
                                    0

                    def findDoorway =
                            if (charAt == 'X') {
                                    hinge = this
                                    r.filter(_.isCardinal).map { d =&gt;
                                            if (p(d).charAt == ' ' &amp;&amp; p(P(d.x * (doorLength + 1), d.y * (doorLength + 1))).isWall)
                                                    d.getCorrectRotation2
                                    }
                            }

                    def getCorrectRotation2: Unit = Seq(r ++ r, (r ++ r).reverse).map(l =&gt; l.drop(l.indexOf(this) + 1))
                            .map(_.take(4))
                            .filter(_.exists(a =&gt; a.p(hinge)isDoor))(0)
                            .grouped(2)
                            .foreach {
                                    p =&gt;
                                            if (p(1) p (hinge)isWall) {
                                                    p(0)add;
                                                    return
                                            }
                            }

                    def add =
                            if (HorizontalDirections.map(p(_) p (hinge)).exists(_.isWall))
                                    result(y * hinge.doorLength + hinge.y)(x + hinge.x) = '.'
                            else
                                    result(y + hinge.y)(x * hinge.doorLength + hinge.x) = '.'

            }

            val size = args(0).size
            Array.tabulate(size, size) { (i, j) =&gt; P(i, j).findDoorway }

            result.map(_.mkString).map(println)
    }


Using OOP was definitely the wrong approach here, in hindsight. If I could do it again I would definitely go with a bunch of hardcoded truth tables.