Strumming techniques?

First, the key difference:
We all learn strumming early on, because it makes sense when playing alone. You can strum a simple song, sing along and get a decent result. As skills progress, you find that regular strumming does not fit very well into an arrangement or mix of other instrument. It takes up a lot of aural space for the interest if provides. An electric guitar greatly extends the possibilities, since the extra volume allows us to play almost anything, even subtle little lines and still hang in mix with horns, drums and so on.

Next, here are a few variations that you might try:

1. Thrumming power chords - using just the heaviest 3 strings, play all downstrokes on some simple power chords, keeping good time. For instance, Pachelbel's canon in D is a natural for this kind exercise: D, A, Bmin, G, D, G, A, etc. Try it with just a smidge of overdrive and palm-muting for cool thumpa-thumpa tone.

2. Ska skanking - using the bridge pickup and a thin, clean tone, try some quick up strokes on off beats, on the skinny strings. Something like "Watching the detectives". Amin, F, Amin, F, C, G, C, G, etc

3. Some U2 style 'scubbing' using a bright tone with a little delay. "In the name of love (pride)" is a good example. Or you could try a descending riff, like in "Just like heaven" by the Cure. It perofrms the same duty as a strumming pattern for keeping time, but takes up less space in the mix, since it is a single note run.

4. Lastly, try some hybrid picking. Hold a pick normally but add in fingerpicking using your ring and middle fingers. This is popular in country music and really makes basic chords sound nice. You will also hear it in everything from Beatles tunes to alternative.