I can't figure out what you are seeing in the device settings.
Ultimately, if you are running out of app storage on the device, particularly one with small overall capacity - say 4 or 8gb, an sd card will only help a little.
So you won't be able to add the apps you want even with a 128gb sd card installed, sorry.
Only chunks of some apps can be moved to the sd card, the app itself will remain on the device and create links on the card to find each portion.
I can't use Storage to move apps, but I can tap on the Used Space section and get a breakdown of the space used. Samsung's have a built-in file explorer called My Files, or a good file app to download is ES File Explorer, and they can help move things around.
The standard way to move an app is to go to Settings - Apps /Applications Manager - All, tap each app you want to move for the App Info screen, and press Move to SD Card if available on that app.
Stock / built in apps cannot be moved or uninstalled usually, you can disable them and stop them adding more data.
If your device does not support moving to sd card, that would be strange. If the Move to SD Card button is greyed out, either that app is not written to be moved, or there is a problem recognising the card. See if the card is mounted and formatted by scrolling down in Storage.
See this guide:
http://forums.androidcentral.com/showthread.php?t=315804
A Samsung Galaxy N3: