The most efficient way to merge two lists in Java
Exception Handling

Your handling is not great.... this is a sign of poor forward planning:


    catch(FileNotFoundException e){}



And this is a sign of something almost as bad:


    catch(FileNotFoundException e){ System.out.print("No Such File");}
    System.out.print("Done!");
    }



The first time I read that, I got confused and thought the "Done!" println was part of the exception handling. You need to work on the indentation. Also, just printing "No such file" is not a very helpful exception handling.

Style

1-liner blocks are seemingly convenient  but in the long term can have negative impacts on maintainability. You have a lot of them, and they make reading your code hard.

Your code is also suffocating due to lack of whitespace. You need to put spaces around operators to help the code to breath.... yeah, that sounds alarmist, but it really helps.


    File newFile=new File("mixOfLists.txt");
    try{
    PrintWriter writer=new PrintWriter(newFile);
    for(int i=0; i&lt;array.length; i++){
        writer.println(array[i]);
    }



should be:

    File newFile = new File("mixOfLists.txt");
    try{
        PrintWriter writer = new PrintWriter(newFile);
        for(int i = 0; i &lt; array.length; i++) {
            writer.println(array[i]);
        }
        ....


Resources

You should use try-with-resources for your IO sources and sinks. As things stand at the moment, you don't close the readers properly.

Algorithm

You're reading both files in to their own sets, and then merging the sets, and then outputting the result.

A better solution would be to use the boolean return value from the add(...) method to determine whether the word has been seen before... consider:

        while(s.hasNextLine()){
            String line = s.nextLine();
            if(hash1.add(line)) {
                writer.println(line);
            }
        }


The above code can be used for both the input files, and only writes out the word if the word has not been seen before.

This way you have only one set, and you do the merge at the same time as the reading.

Also, you should be using Java 8 streams..... hmmm... that would be nice.