Hi, and welcome!
Not all apps (and not all of apps that move) can go to the sd card. And cache and data also store on your phone's internal memory.
Clear the cache and what data you can ( but be careful with data, as it holds all your information--like the password and any data that is yours alone, such as scores in a game.)
Go into Settings-->Apps and check each app. There will be a button to clear the cache and data, as well as one to move the app to the sd card is that option is available. (Don't move widgets to the sd card, even if they say they will go--it makes them wonky.)
There are also apps in the Play Store that will help you do this. Supertoolbox has utilities that do it, and it is free and you do not need root to use it--but it will take up room on your phone.
A good place to look for a quick way to free up memory for me is clearing the data from the Play Store (especially after several apps update) and any news sites. And the browser(s) I use.
You might also join forums, find the S2 folders, and ask others who use your specific phone. Folks on here are friendly and helpful.
Hooe this helps.