(long, medium, short, rest) better than (rest, short, medium, long) running to strengthen my quads?

why do you think your quads are weak?

running is not really a quad strengthening w/o anyway.
The usual ST way to stronger (bigger) quads is cycling. I suggest sprinting more than we typically do. Think Chris Hoy, he’s got massive quads.
alternative route: run downhill, a lot , with the eccentric quad contractions, you will have bigger, sorer quads right away

usual way for other folks: wt training. quad extensions (ugh) are decent. I prefer lunges and bulgarian split squats (http://www.menshealth.com/fitness/the-worst-way-to-perform-the-bulgarian-split-squat), mostly b/c I like saying that I do bulgarian split squats. They sound really hardcore!