This will probably take a lil time(make that alot of time)
You seem to be on the right track with the single string songs, and asking here for help will always yield good results.

I think the next step for you is to learn a major scale and then start playing the single string songs you know as root and fifth power chords...for this, place your index finger on the original string and fret that you would have to play the son on just one string...then add your ring finger to the string directly above(in pitch, below in actual distance and physical position) that string,but two frets higher on the fretboard...so as the songs you know use only the lowE string, you will place your ring finger two frets up, but on the Astring...you with me? start very slowly, and dont worry, you wont be able to play with seamless changes initially, infact, you will probably not be able to move this chord position at all to begin with, but take some time on it and it will progress...
sorry if that is a bit hard to understand, it is rather hard to explain these things without being able to show you what I am talking about...

Good Luck.