My Hair cannot curl...

Have you tried not washing it for a few days before? if your hair gets use to it, it will not appear greasy and will hold a curl a lot better! this is the only way mine will stay!

Before you go perm (which is adding chemicals to your hair and is permanent -- hence the name), have you tried a roller set? Try going to a salon and tell them you have curl resistant hair and you want a roller set. They will put your hair on rollers, while it's wet and sit you under a hood drying. This will heat set your curls and maybe make them stay longer. It's worth a shot and way less of a committment than a perm. Also, regarding clip in extensions, there is a way to get extensions put in without actually having your natural hair mixed in. A good stylist used to doing extensions, will braid your natural hair up and clip the extensions to the braids. They can do this in a way that allows the front portion of your hair to be teased up with added volume but the back left out for a nice half-up/half-down do. You may have to do a bit of searching for someone in your area who can do this and I can't tell you what the cost will be, but i'm just throwing some other options out there.

Yes, I do this as well. I have thick, long, straight hair, and a lot of of it, cant do buns, neck kills me an hour into it. The dry shampoo helps add that grit and give the hair texture, you can try with a wand curler at home. You can also try with a bit of hairspray to hold that curl some. Hope it works for you if you decide to give it a go.