The best shampoo to use it an herbal shampoo followed by a regular conditioner.
But if you can't find an herbal, Aveeno is your next best bet.
Also...over washing your hair can only superseed the problem because it triggers oil production when you are constantly trying to wash it out.
I do know that Caucasians have a different textured hair than those of natural brown skin, or Africans. I have really thick hair, and because of that my hair doesn't get as greasy as a lot of my white friends, who feel the need to wash it everyday.
Actually you shouldn't wash your hair everyday, you're suppose to wash it every other day to keep it healthy.
Anyways...to overcome it, i suggest putting oil in your hair. Herbal hair (Indian hair oil) is the best, if you have an Indian store close by. If not, simple baby oil will work (but make sure is the plain kind) Put that in your hair and wash your hair once every two days (do not wash it everyday). Yeah I know it sounds like you're just adding oil, but its a different kind. Don't wash it everyday, and only brush your hair twice a day. Some people over brush their hair causing oil to spread quickly from the roots down, making it seem like its over oily when its not. But do this for about two weeks...and soon you will see that its less greasy.
The baby oil also makes your hair healthy again, making it stronger, thicker, and shiny.