How can I make my not straight hair wavy?

Okay, I have hair issues. My hair is thick and long (but not ridiculously long) which I love but it isn't straight, curly, or wavy. It's basically just not straight with waves sometimes. I want it to be reliably slightly wavy but I don't want to use any heat (including blow drying, I let my hair air dry). Also my hair is REALLY oily. I would rather my hair not be crunchy but I don't really care. Do you have any suggestions?