How to find out what algorithm [ encryption ] are supported by my JVM?

The following will list all the providers and the algorithms supporter. What version of Java are you using? Unless you’re on an old version JCE should be included as standard.

import java.security.Provider;
import java.security.Security;

public class SecurityListings {
    public static void main(String[] args) {
        for (Provider provider : Security.getProviders()) {
            System.out.println("Provider: " + provider.getName());
            for (Provider.Service service : provider.getServices()) {
                System.out.println("  Algorithm: " + service.getAlgorithm());
            }
        }

    }
}

Edit:
Any reason why you don’t use the standard stuff from the javax.crypto package?

1) Generate a Key using

Key key = SecretKeyFactory.getInstance(algorithm).generateSecret(new PBEKeySpec(password.toCharArray()));

2) Create a Cipher using

cipher = Cipher.getInstance(algorithm);  

3) Init your cipher with the key

cipher.init(Cipher.ENCRYPT_MODE, key);  

4) Do the encrypting with

byte[] encrypted = cipher.doFinal(data)