[Azhia]

Michelle,

Yes, it is normal for hair of your texture to become oily after several days of not washing.

Stick with setting the hair, as suggested by Zumarrad, as opposed to heat (that's good you normally stay away from it, keeps it healthy) and I also agree with her suggestion to maintain layers, or at least some good texturizing, to keep the weight to a minimum without sacrificing length.

Curl does not stay in my hair either. What I used to do (when I had hair) was keep textured long layers; a few hours before a show I'd wrap my hair in at least 2 tight buns with some product (less is more, actually) and then let it out before performing. I could do this either dry or wet and then let it dry. Try the Bumble and Bumble. They have wonderful curl enhancing products that will not make your hair oily, or cut down on product. Not that much is needed for desired effect.
Regular trims is the only solution for split ends. There is no product that will take them away, unfortunately! And when you do get it cut, make sure the stylist does not do any "slicing" or "channeling", basically anything where the blade (shears or razor) "slides" along the shaft...split end city for sure! I am very prone to split ends and once I knew to tell my stylist to not do any kind of sliding, I have had no split ends and can allow my hair to grow without having to trim it as often.
Let us know how it works!