I don't think this is a typical strata quilt because the squares do not have repetitive fabric sequences in them. Here's how I would go about re-creating it.
Start with a large rectangle of freezer paper. Draw wavy lines going in the same direction, using a permanent marker. Make registration marks along each line, so you can match up the pieces later. Label each piece in order A, B, C, D, etc.
Cut the freezer paper along your wavy lines.
Iron the wavy freezer paper pieces to your fabric of choice. Cut the fabrics 1/4-inch to 1/2-inch away from the edge of the freezer paper.
Piece the strips back together. This is when the strip labels and registration marks will help you line them up. At this step, you have to decide on your piecing technique.
What I would probably do is machine applique a la Harriet Hargrave, using glue to turn under the edge on one strip and appliqueing it on top of the seam allowance of the previous strip. (This is where it would be helpful to have 1/2-inch seam allowance on the non-turned under strip, although not strictly necessary.)
Alternatively, you can piece as usual, pinning the strips together, using the freezer paper edges to help with accuracy, snipping as necessary so curves fit each other. I think this would be harder to do; however, might not be that hard as long as your waves are kept fairly shallow. With deep waves, you might have to piece in sections from first one side and then the other (because of the difficulty matching concave and convex curves).
Once the wavy strata has been created, cut your squares out. These would be cut "on-point" (on the diagonal of the strata), and you would place your square template at different places all over the strata so that each square will be different. You would then remove the freezer paper before sewing the squares together.
You might need to create several different strata to get all of the squares you want.