Try something like this:
// function to remove the Links menu item
function wpse_7192_remove_menus()
{
// setup the global menu variable
global $menu;
// this is an array of the menu item names we wish to remove
$restricted = array( __('Links'));
end ($menu);
while (prev($menu))
{
$value = explode( ' ', $menu[key($menu)][0] );
if( in_array( $value[0] != NULL ? $value[0] : "" , $restricted ) )
{
unset( $menu[key($menu)] );
}
}
}
if(!current_user_can('edit_pages'))
{
// hook into the action that creates the menu
add_action('admin_menu', 'wpse_7192_remove_menus');
}
That will remove the links menu for everyone except those that can manage options (which I believe is the Editor level).
So just follow this same logic to remove all the necessary menus for certain user levels.
Check out the post here for further details.