What are the strongest encryption/hashing functions?

Hashing has nothing to do with encryption and CI_Encryption doesn't provide hashing. But to answer your question: bcrypt, scrypt and pbkdf2 are today's standards for password hashing. The first one is the most accessible and popular in the PHP world, just use the password hashing functions.

There's no "strongest" encryption, but AES-128 is a the de-facto standard everywhere (except maybe in Japan). It's also the default algorithm in CI_Encryption, so all you need is to use a strong key and encrypt()/decrypt() away.