The way I would approach this is with a machine applique technique using freezer paper. The "dog lady" uses this technique for her quilts. Here is a link to her nature quilts:
http://www.malec-designs.com/nature10.html
I won't go into all the steps here, because I'll probably forget some small but critical step! But basically you use the freezer paper as a master applique template. Use glue or paste to turn under the edge of a new strip (a la Harriet Hargrave machine applique), then machine applique it on top of the rough edge you have left from the previous strip.
As far as I know, this would be the best way to sew lots of wavy strips together.
It might be possible to piece them instead, again using freezer paper. In that case you would still draw a master template on freezer paper, but then you would cut apart the strips, iron them to the wrong side of fabric, cut the strips out 1/4" away from the freezer paper, then piece them together at the machine using the edges of the freezer paper as your guide. I think that would be a lot more difficult, though.