What [scale] could I use?
Single scale option
All of the answers generally revolve around noticing which notes are in the chords you're playing. @PauloHenrique was most explicit about this. So let's take that solution a step further. Looking at the roots of the chords gives:
E F G _A
Similarly, the chordal fifths give:
B c d _e
Combining them gives us a very intriguing eight-note (octatonic) scale.
T:complete scale on E
E F G _A B c d _e
Running this scale over the power chords gives a sound I personally like a lot, but when you hit the Ab chord, start the scale on F, because starting on E against the Eb doesn't fit the overall sound.
In fact, this scale works even better if you start it by running over the chord fifths. In that case you don't have to adjust when you get to the Ab chord.
T:complete scale on B
B, C D _E E F G _A
Two-scale with transposition options
There are two cases where three of the power chords fit a single diatonic scale:
E F G and
F G Ab. The other two cases can't fit a single diatonic scale, because they contain two consecutive half steps:
G Ab E contains
D Eb E and
Ab E F contains
Eb E F.
E F G
All three of these power chords will fit into C major. I recommend using B locrian for the best result, because that way the root and fifth (
F) correspond to chord tones (5 of E, Root of F, 3 of G).
In that case, I like C minor for the Ab chord, as it mirrors the half-step shifts in the chords, especially from G to Ab.
F G Ab
Here we encounter F minor, as has been discussed, but in the form of Dorian, to accommodate the D in the G chord. For compatability, use E phrygian on the E chord to set up the F and G chords plus the D in the next scale.
C natural minor
Use B Phrygian against the E chord. It's gives a sense of a C major/minor shift, but the
B-F# perfect fifth sounds better against the E chord than
C harmonic minor (starting on B)
In this case, use B Locrian over the E.
Partial scale options
Rather than try to fit a complete scale to the chords, you can find subsets of scales that work well, often avoiding some of the "bad" notes that don't fit one chord or the other. Try running either of the main four-note subsets of my first solution over the entire set of power chords:
E F G Ab or
B C D Eb.
What am I missing
I don't think you're really missing anything. There are rules of thumb like power chords tending to sound minor and examining the complete collection of notes to derive/build scales, but in the end it's trial and error to find what you like. To construct triads, you can then extract them from the scales you've chosen.
However, in this case, I find triads limiting. As soon as you add the third to these chords, you create conflicts that generally restrict your options for scales/melody.