Welcome to the Board! I had to look up the quilt. It is very pretty.
How big are you planning to make it? An entire quilt or a wall hanging?
Can you post a picture of what you've done so far? I don't know how this quilt is put together, so I can't help you that way.
If your fabric was not straight of grain when you cut it, you may have had a bow in your strips to begin with and therefore your strips would in turn, not stay straight when sewn together.
If you have to sew long strips together into strip sets, try sewing two strips together into sets at a time, then sew those two to another two and those four to another four until you've got what you need. If you just sew long strips 1 after the other, they do tend to go wonky.
I don't think taking it apart is going to help, myself.
I would do as others suggested, but get yourself a yardstick and spray starch and spray what you want straight, let sit 30 seconds and then push it up straight against the yardstick. Don't pull the length, just make it behave against the yardstick length. Remove the yardstick and press it carefully to keep this straight edge.
Also, when you put your sashing between the braids, that will help some.
I really think a picture might help, if you can swing it.
Good luck and let us know!
Watson