You can use the Base64 version of your image and send it like this:

onLine[data.to].emit('newPrivateMessage',{from:name, img:data.img.toString('base64'), type:'Private Msg'})

.. and then on the client side receive it and create an image

socket.on("newPrivateMessage", function(data) {
    if (data.img) {
        var img = new Image();
        img.src = 'data:image/jpeg;base64,' + data.img;

        // Do whatever you want with your image.
    }
});

UPDATE

The following is a snippet taken from the link I've commented below. As you can see it takes the image from the input, reads it and sends to the server. After that you can send the same data from the server to another client.

For the full example, please read the article.

JavaScript (client)

...

$('#imageFile').on('change', function(e) {
   var file = e.originalEvent.target.files[0],
     reader = new FileReader();

   reader.onload = function(evt) {
     var jsonObject = {
         'imageData': evt.target.result
       }

     // send a custom socket message to server
     socket.emit('user image', jsonObject);
   };

   reader.readAsDataURL(file);
 });

...

HTML

...

Image file: <input type="file" id="imageFile" /><br/>

...

UPDATE 2

Here is one example I have found:

Java (client)

File file = new File("path/to/the/image");

try {
    FileInputStream imageInFile = new FileInputStream(file);
    byte imageData[] = new byte[(int) file.length()];
    imageInFile.read(imageData);

    // Converting Image byte array into Base64 String
    String imageDataString = Base64.encodeBase64URLSafeString(imageData);
} catch (...) {
    ...
}

The above snippet shows how to read the file and encode the data into a base64 string. So then you can send it just like a string (I assume).

Here is the complete example: How to convert Image to String and String to Image in Java?

Also I have found encodeToString function of Base64.Encoder (java.util package), which you can use.