Out of several, I shorlisted two options :-
So far, these are the two android file encryption apps that do not ask for permission to access internet in your android.
Both of them use AES encryption and securely wipes the original source file once encrypted.
I have not trial-ed Droid Crypt. It requires you to specifically install IO file manager to work and appears to have a more convoluted interface compared to Encrytion Manager. IO file manager is free. It's a basic but very functional file manager. However, I use and prefer ES File Explorer.
For the timebeing, I have settled on Encryption Manager. It works very well on my Samsung Galaxy S2. Had several correspondences with the developer (Hans Schuell) who was very patient and responsive with all my questions. Of note, Encryption Manager uses SHA-1 hash generator for your master password to access the database and generate encryption keys for encryption in either AES-256 or Twofish algorithm (your choice). There is some reservations about the strength of SHA-1 but making sense of all the technical jargon, I found this post that explains it more or less in a relatively layman-friendly manner :-http://stackoverflow.com/questions/2772014/is-sha-1-secure-for-password-storage
There is a helpfile within Encryption Manager that explains why you should have a long and strong password for your Master Password. I made mine at least 256-bit because I'm somewhat paranoid. While I also use KeyPassDroid as an AES-256 encripted password manager for all my passwords, I do not recommed you use the copy to clipboard function of KeyPassDroid in a Samsung Galaxy. As I mentioned earlier, the Samsung Galaxy is setup in a manner that does not allow its clipboard to accept an empty value. Consequently, while KeyPassDroid will successfully clear clipboards in other mobiles upon exit, it does not do so properly in the Samsung. I find that I have to manually clear the clipboard using Samsung's Polaris Desktop tool and also using the Airdroid app to access the clipboard to clear the final clipboard value before everything is successfully cleaned.
So, if using KeyPassdroid, I will just open the app, view the password, write it down on a piece of tissue, access the specific account with the password without copying to clipboard. When I'm done, I will just wet the password on tissue (spitting adequately on it is fine). The ink will run and the tissue and writing, when soggy, will disintegrate when you rub it.