How to resolve Catchable fatal error in entity.inc?
In case anyone else has a similar problem, here is how I solved it. I began by using Drush to disable the commerce modules one after another (in the correct order) to detect which module caused the error. I got so far that in the end I had disabled all the commerce modules, plus Rules and Entity token. And still the same error message was showing (the first one in my question). 

I suspected that I really needed to flush all cache, but I could not reach any page in the site, and still it was not enough to truncate all the cache tables in the db and to run Drush cc all. So what to do? I finally found a way to flush all caches with this snippet (https://www.drupal.org/docs/7/administering-drupal-7-site/clearing-or-rebuilding-drupals-cache) in a file named for example clear.php in the web root:

&lt;?php
// Define static var.
define('DRUPAL_ROOT', getcwd());
// Include bootstrap.
include_once('./includes/bootstrap.inc');
// Initialize stuff.
drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL);
// Clear cache.
drupal_flush_all_caches();


After saving the above file in the web root, you can just navigate to it whith the browser. In my case I also had to comment out all the memcached rows in settings.php in order for this to work (I got a "Cannot redeclare ..." error message).

When I finally managed to flush all caches this way, the site began to work. I still don't know how I would have done this otherwise. And "Flush all caches" obviously does somehting more than what is accomplished by executing drush cc all + manually truncating all the cache tables in the database.

So if anyone else has a similar problem with white screens and error messages, first try to flush all caches with the method above. And if you use memcached, you will have to comment out everything that regards memchached in settings.php in order to do this.