So I'm at the point right now where I am just playing a few new songs a week. I know the majority of the basic chords. I can do some power chord stuff as well (Smells like teen spirit, All the small things, etc.).

Whenever I sit down to practice, I work on a lot of finger strength and dexterity stuff, not really knowing what else to do. I do hammer ons, pull offs, going though the minor pentatonic boxes. What else should I be doing? Do you have any song recommendations?

My friend who I have been subtly learning from told me to learn Behind blue eyes and Classical Gas. I didn't have a problem with Behind blue eyes but classical gas is quite a bit tougher.
Go neo....start learning all kinds of classical music. I strongly suggest looking into Niccolo Paganini and stuff like that.
um. i say teach yourself. ive never looked at a guitar book, never taken a lesson. and im a rather decent writer. and learn all of the songs you play by ear then compare what you play to tabs. it helps soo much to be able to learn stuff by ear. eventually playing comes natural.
I am teaching myself. When I say learning form him it means I jam with him once a week or so and pick up on some new tips and tricks.