Ok, I found a solution.
The main issue was due to the fact that when I installed the demo content the website was only in English and all the products has been stored in the virtuemart_products tab.
Adding second language the system created two different product tabs (virtuemart_products_en_gb and virtuemart_products_it_it), so when I deleted the demo products they disappeared from the new language tabs but, somehow, not from the main one (virtuemart_products).
I simply edited the database (with phpMyAdmin) and deleted all unwanted products from the original product tab.
Now it seems to work fine.