How can I make songs I delete in iTunes also delete songs of synced devices?
You have to understand that iTunes is the 'master' in all this, the mobile devices merely 'slaves'.
Anything you do in iTunes will be reflected in the mobiles when manually synced. 

The question you linked is for 'what to do when this sync misbehaves?' &amp; is not the same as your situation. 

Your issue really stems from your iTunes library not being complete, removing the simplest option from your choices. Google 'iTunes iPhone copy' for a slew of apps that will transfer songs from the mobile to iTunes, then you can go back to doing it the recommended way - by syncing with iTunes.