Lucky you to have been given so many boxes of such a vaiety of fabrics!! There are so many uses for all the different types and textures - many have already been mentioned. Depending on what you make and how often you think it will be washed, it is good to see how it washes for normal use and use a wider seam.
We had a drive to make placemats for Meals on Wheels - needed 258 - Some of our guild members made placemats with the patterned polyester fabrics and seersucker with batting between. Some of the solid colors had machine applique on top for the fronts and polyester ginghams or patterns for the backing and some were done in wide strips/bands of different colors - didn't look bad or shabby.
Another guild member uses plain polyester curtaining material that isn't slippery as a base behind her clam shell quilts and other similar patterns. She sews the pieces to the base in rows and then sews the rows together then adds her batting and backing and then LA quilts them. She says she finds it easier to work with - she coud use muslin but she was given a lot of curtaining yardage and she is using it up.
One guild member who is very artistic used a variety of upholstery fabrics to make a few beautiful art quilts. She created her own designs and they have a variety of textures and colors - wish I had a pic to show! They were very unusual and amazing - she is a talented quilter with lots of creative ideas!!