Show a menu block only on nodes that belongs to this menu I am trying to accomplish something similar to the book navigation module.

Say I create a block containing a menu. I want this block to become visible for nodes that belong to this menu.

So if NodeA belongs to the menu "My SubMenu 1", which is included in a block called "My Submenu 1 Block", I want this block to appear everytime NodeA comes up.

This could be accomplished with some pathauto tricks, or assigning a certain taxonomy term to all nodes of "My Submenu 1". But I realise this is redundunt, there is no need to force the user to create content with specific terms--the information is all there in menu-->node connection.
Take a peek at http://drupal.org/project/menu_block. I think it might do what you want, or, if not, at least maybe its code might give you an idea on how to do so yourself.