First off, you've got some naming issues. Your classes need to be singular: category, product, and product_image. (The tables, however, need to be plural.) With the updated inflector helper, DMZ will handle the name conversions. You'll also need to update your $has_one and $has_many arrays in the same manner.
Then, you access them like this:
Code:
$cat = new Category($cat_id); // or find it in a loop, etc.
$products = $cat->product->get();
foreach($products as $product) {
$product->product_image->get();
// now you can loop over the image
}
Of course, you can look up a product directly.
Take a look at the example code included with the example application. It was in the full download. There are examples of all of this and more.