Java code to delete whole Binary tree.

root = null

C++ isn't garbage collected, but Java is. In Java, once an object no longer has any references to it, it will be automatically removed from memory. All of the referenced objects of the garbage collected object will also be removed if they have no other references to them. That bit addresses your question: if the nodes under root don't have any external references, they will be automatically removed after root.

Trivially root = null;. However there is a difference with C++ as Java cannot change a passed variable:

delete(root);

will never set root to something else. This was a design principle to make Java more qualitative in software engineering sense (less error prone) than C++ (Node*&).

You need to use return values, as there are no output values. A modified example:

Node deleteSubtree(Node tree, Object value)  {
    if (tree == null) {
        return null;
    }
    if (value.equals(tree.value)) {
        return null; // Deleting a subtree
    }
    tree.left = delete(tree.left, value);
    tree.right = delete(tree.right, value);
    return root;
}

NOde root = ...
root = delete(root, "war");

This would delete the subtree rooted at "war".

You simply need to unlink the left and right nodes from the root:

void delete(Node root)
{
    if (root!=null){
        delete(root.left);
        root.left = null;
        delete(root.right);
        root.right = null;
    }
}

Setting root to null is useless, because it is a local variable that will be unlinked when the method returns anyway. Also it does not affect the value in the calling method, so it has no effect at all.