I think we're missing some information here. Specifically, your hair texture and density -- are your individual strands fine, medium, or coarse, and how many strands do you have, which is usually classified as thin, medium, or thick.
People with fine, thin hair typically have more problems with oil, and the common advice to wash less often doesn't work well for them unless they grow their hair long and then learn not to disturb their scalps. I have baby fine, thin hair. The joke around here is that my hair tangles when I breathe. When I was younger it would have been classified as type 1a, but in post (early) menopause it now has the slightest bend in a few areas, so it's more type 1a/b. If I curl it, the curls fall out (can be maintained by using product before curling and hair spray after, but even then will mostly fall). If I sleep with it braided or twisted, it will start out with some wave and then fall out.
I've tried just about everything over the course of the past 30 years. All natural shampoos and conditioners, soap based shampoos, shampoo bars, Dr. Bronner's soap (diluted), egg yolks, honey, baking soda and apple cider vinegar, clay, soap nuts (soaked into a liquid solution), conditioner only, water only, and others I've certainly forgotten. I've gone as long as a full month with water only, hiding my greasy hair under scarves. Baking soda (diluted, of course) made my hair dull and so fragile it was breaking off. Apple cider vinegar rinses (post baking soda washes or soap based shampoos and shampoo bars) made my hair a grease pit. Truth be told, washing with egg yolks or honey will cleanse my hair, but washing hair with food is expensive. My hair looks fine with conditioner only, but over time my scalp doesn't like it and gets itchy.
I could never wear my hair short like the typical mens cut -- I would be oily within the hour. It's not because I produce tons of oil, but because fine hair is slippery and the oil coats the shaft quickly, and with thin hair there are fewer strands to take the oil.
Anyway, here's what I've learned, in case you have fine thin hair as well.
1) If your hair is short you may have to wash it everyday if you can't stand the sight of oily hair. I don't wear bangs/fringe because I don't want to wash them daily. But if you wash it daily you need to find a way to do it without drying out your scalp. One option is to wash with shampoo one day, and then use conditioner only for a day or two, then wash with shampoo, etc. Watch for itchiness or dandruff, though.
2) Don't stimulate your scalp! I have long hair. I wash my hair every 2-3 days during the warm/hot months and every 3-4 days in winter, which is a huge improvement, but I didn't achieve this until I stopped taking a brush or comb to my scalp everyday. The advice out there to use a boar bristle brush to distribute the natural oils made my hair greasier than ever. I can't preen, either. If I touch my scalp a lot it will get oily. The key is to leave it alone. If I was a man I would probably choose a basic buzz cut so all I had to do was dry my hair with a towel and be done. For long hair, rinse it with cold water if you can -- I find this makes detangling much easier which means less scalp stimulation. Using a blow dryer also stimulates the scalp and can contribute to oiliness.
3) The advice above about growing your hair long is spot on, especially if you are blessed with fine hair but an abundance of it. My young adult son has my hair strand fineness, but it's wavy when longer (not just a little shaggy long, but past the collar) and downright curly when shoulder length or longer. Since he's young he has a lot more strands of hair than I do, but it's still fine and it still get oily looking fast. He's been wearing it long for several years now, and the man bun is his friend. Even if his hair is oily, he has enough hair that when it's pulled up the oil just looks like he has healthy, shiny hair because no scalp shows through. It's a little harder for me since I don't have as much hair. I still mostly wear my hair up or braided, but while we have the same length hair (both of us at about 32" at present), his man bun looks full and my bun is small for how long my hair is.
4) If all of that is too fussy, use product. Cut the top a little shorter so it doesn't flop over or lie flat. Using something like mousse or gel will coat your hair strands, which somewhat stops the oil from sliding down the hair shaft. Or use dry shampoo -- it's not expensive and with short hair one can should last a long time. But be warned that using product will definitely put you into the wash your hair everyday camp.
Finally, when you say a light breeze makes your hair stand up, are you dealing with static electricity? It takes trial and error to find a shampoo and conditioner that prevent static electricity, depending on hair type.