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If you want to move everything, have a look at using AffineTransforms
Transforming Shapes, Text, and Images (The Java™ Tutorials > 2D Graphics > Advanced Topics in Java2D)
Have your MouseListeners...

Change the x,y coordinates of the drawn object. There are hundreds of ways to implement this, and I'm still unclear if you want to move a single object or all of them at the same time, so I recommend...

For listening to Mouse actions, see
How to Write a Mouse Listener (The Java™ Tutorials > Creating a GUI With JFC/Swing > Writing Event Listeners)
How to Write a Mouse-Motion Listener (The Java™...