Anagrams for a given input
I'll focus on the heart of your solution first, which is your readFile() method.  Here's how I would write it:

public static List&lt;String&gt; anagramsInFile(String word, File f)
        throws FileNotFoundException {
    char[] canonical = canonicalize(original);
    ArrayList&lt;String&gt; anagrams = new ArrayList&lt;String&gt;(); 
    try (Scanner s = new Scanner(f)) {
        while (s.hasNext()) {
            String candidate = s.next();
            if ( (candidate.length() == word.length()) &amp;&amp;
                 (Arrays.equals(canonical, canonicalize(candidate))) ) {
                anagrams.add(candidate);
            }
        }
    }
    return anagrams;
}

private static char[] canonicalize(String original) {
    char[] array = original.toCharArray();
    Arrays.sort(array);
    return array;
}


Points to note:


Naming is important.  handleFile() is vague; anagramsInFile() is meaningful.  Also, I find anag to be confusing parameter name.
Hard-coding the filename inside the method is a bad idea.
Unless the caller has a reason to require an ArrayList, your method signature should just commit to returning some kind of List.  Better yet, consider returning a Set.
You only have to canonicalize the original string once, not once per word in the file.
Canonicalization deserves a helper method, since you have to do it to both the original string and to the contents of the file.
Canonicalizing to a char[] avoids working character by character, since you can take advantage of String.toCharArray().  It's probably more efficient as well.
There's no point in maintaining k: it's just the size() of the returned list.  Maintaining k as a class variable is particularly egregious, as there's no reason for that count to be part of the state of the class.
If your blocks are so lengthy and deeply nested that you need comments on the closing braces, consider that a Bad Code Smell and address that issue instead.  (By the way, your braces were misaligned, which causes confusion that even your close-brace comments can't compensate for.)


Next, let's look at getOutPut().  Here's how I would write it:

private static String formatOutput(List&lt;String&gt; words) {
    StringBuilder out = new StringBuilder('[');
    int wordsPrinted = 0;
    Iterator&lt;String&gt; w = words.iterator();
    while (w.hasNext()) {
        out.append(w.next());
        if (w.hasNext()) {
           out.append((++wordsPrinted % 8 == 0) ? "\n" : ", ");
        }
    }
    return out.append(']').toString();
}


Points to note:


When concatenating so many strings, you really need to use a StringBuilder.  Repeated string + string would create a temporary string each time.
Your output is buggy: you drop every eighth word, replacing it with a newline.
Be careful with edge cases: your code crashes when words is empty.
Try to structure your code so it's obvious that certain properties hold true.  For example, in my solution, you can see that every word gets printed (because if .hasNext() is true, the next word will get appended).  You can also see that every word except the last word is followed by a delimiter (either newline or comma).
Avoid cryptically named variables like x and y.  In fact, you don't even use  y.
Naming your result wordz when there's another variable named words makes the code a pain to read.


Finally:

public static void main(String[] args) throws FileNotFoundException{
    String word = input("Enter the word or words you would like to be processed");
    List&lt;String&gt; anagrams = anagramsInFile(word, new File("words.txt"));
    display(String.format("The word %s has %d matches.  They are:\n\n%s",
                          word, anagrams.size(), formatOutput(anagrams)));
}

private static String input(String prompt) {
    return JOptionPane.showInputDialog(null, prompt);
}

private static void display(String message) {
    JOptionPane.showMessageDialog(null, message);
}


Observations:


I've decomposed the work differently.  There's input() and display(), which are analogous to each other, and encapsulate the Swing UI.  (If you ever want to convert the program to work in the text console, you just modify those functions.)
More importantly, you can now see at a glance what the whole program does just by looking at main().  Note that all string constants are there as well: the prompt, the filename, and the output.
Don't declare any more variables than you need to.  If possible, when you declare variables, assign them in the same statement.
Use String.format().