Hair care, how to keep hair from looking limp and greasy between washes?

Female, with straight (slightly wavy) shoulder-length hair which I sometimes grow out, usually dyed. Most everything I read indicates that washing your hair every single day is actually unhealthy for the hair. So I wash mine every other day, not skipping more than a single day in-between. However, the day that I don't wash it, my hair is limp and uncooperative, and near the scalp it looks greasy (to my eyes, at least). I use very few hair products, just a good quality shampoo and occasionally a spritz of hairspray when necessary. I don't use heating appliances on it, no hair dryers or curling irons.

Any suggestions as to how to keep my hair from looking and feeling gross on the day I don't wash? I hate going to work like this; I feel icky! And when I step outside and there's any wind or rain, I'm pretty much doomed to look even worse for the rest of the day, lol.