First let me say I like your hair and if your thinking about cutting it how about maybe shoulder length. You could have it layered. I think that would look really nice. A girl I work with had hair similar to your and she did that and loves it and it looks great.
As for the greasy part, aside from washing it every day have you tried Neutrogena Anti-Residue Shampoo? I find this works really great to get out all the products I put on my hair that can weigh it down and make it look greasy. Good luck on finding a product that you like and finding the cut for you (I find just asking my hairdresser what she thinks is a good cut works great). Here's a nice site with lots of great hair styles...Beautiful Haircuts

Now as for the poll I didn't pic. I don't really "hate" my hair but definitely don't love it either. I wish I could grow it longer and it would look nice, but now it seems my hair has aged. It's so much different feeling than when I was younger....I'd love to have my "young" hair back