How do I unwrap correctly? Blender noob here. Made a very simple vector square with radiused corners in Inkscape,and saved it as a simple SVG.

Imported to Blender 2.77, changed it to a mesh. Scaled it, then extruded it along the Z axis.

Blend file: 

Marked a seam, hit unwrap. The resulting shape looks like a twisted towel.
Only the project from view (ortho),remotely works.
What am I doing wrong?
I took a look at your file, and the first thing I did was remove doubles. Select all in edit mode, press W>remove doubles (or just press  R). Second, I recalculated normals with  Ctrl+ N and then I unwrapped with Smart UV project. I think that this will be the best way to go for you. This is the result you can expect: