Good ideas here, but I'm with Marianne, it's likely that some of the grains were off when you cut them and needed to be prewashed, stretched diagonally to straighten, starched and ironed into submission, then use a walking foot if needed to keep them from getting stretched. After that, block it square before sandwiching and maybe use a little more quilting than you normally would. If the back is nice and square, and you sandwich it well, it will probably maintain squareness with quilting and blocking. Good luck there.

How far is the quilt to completion. Can it be blocked? Incorrectly sewn borders and binding can also make for a wavy quilt.

There are lots of reasons posted here for your consideration, each one being a lesson in itself, from fabric preparation, cutting technique, to the perfect quarter inch, ironing technique, grain line. It has taken many of us years to learn all of these lessons. Be patient with yourself, and know that our best friend is the seam-ripper for areas that will bug your forever. The term "creative piecing" is used by some to describe wonky piecing. Non-quilters will never notice.

Enjoy the learning process. There are great short lessons on all of this in the various Classrooms.

I have noticed that a lot of fabric nowadays are very skew-whiff. I am first and foremost a dressmaker so am very conscientious about grain lines. Sometimes even after washing it is so skewed that you have to do some hard pulling to get it straight. If you have cut strips from a piece of fabric that have gone onto the bolt skewed I can see it "moving" when it has gone on the wall. It is like a skirt on the bias that needs to hang for a couple of days before you hem it. Next time you may consider hanging the top before trimming unless you want to go to the trouble of making sure your cuts are on grain.
Marianne

I don't do this because I love to handle soft fabrics, but I know several quilters who spray starch all fabrics before they cut and sew them.

And sew from alternating ends

I'm assuming that your seams are straight and even. If not, that could be the problem. Otherwise, remember that there is some stretch along WOF and that stretch may differ for each fabric. In the future, you might want to use a walking foot to avoid pulling and stretching. If you don't have a walking foot, try pinning parallel rather than perpendicular to the seam line while fabrics are laying flat and even on your cutting table.

I hope this helps.

I'm a fan of making strip quilts especially for the great nephews nieces. The pattern that I use calls for 10" of 8 fabrics and they are usually from different designers. Each fabric is cut into 4 specific widths from the WOF. On the latest quilt after sewing all the cut strips together starting with the Salvaged edge that was even and would be trimmed afterwards, I found that my quilt was not hanging straight at all. I've never had this problem before.

Any ideas???