Internal storage is used up by Android My Xperia J has 756 MB of internal storage. After 2 months of use I hardly can install anything as my system directory is 600 MB. It seems that in system/apps I have 200 MB of not used apk files (system apps that could be activated I guess), and 400 MB of the system with its core and its installed apps. So basically 756 MB is around 200 MB at the first instant of starting the using of my phone.

I use Clean Master to delete 10-20 MB of cached data now and then but as my phone is not rooted, I am stuck. I moved every application to the internal SD card (I can't use the external SD card - because it is not listed in the application settings as an option)

What can I do to install more apps?
Unfortunately this is a common problem for all xperia J users, including myself. I have installed many recommended apps for moving stuff from internal to external SD card but after doing this, pictures, music, videos etc I have moved cannot be played/viewed meaning you have to move them back in order for them to be viewed/ played again, however adter moving them back my files still didn't work. I have not yet come across the answer to solving this problem but I can recommend not downloading apps that move stuff to SD card as they won't work, just clear your cache as much as possible to relieve it of some memory. Hope this helps a little bit