You will need to write your own ImageCache
implementation if you use Volley.
If you want an integrated implementation that you have the most control over, use Volley. There's probably an implementation out there for ImageCache on GitHub already.
If you want a fast way to load images, use Android Universal Image loader or AQuery. If you haven't tried already, Android Universal Image Loader works quite well.
EDIT
There's a good implementation of the ImageCache interface here:
This requires the support library.