I am looking for suggestions of some useful purpose for all these left over strips
Just curious, how wide are the strips and how long? And not to doubt you, but what are your talents? I have been gathering up odd pieces of wood, oh- forever, and have done a lot of things with them. I have made boxes for storing things. Kind of like a pull out basket for a shelf. I have also used them for building shelves and making toys for my kids. You could also cut them into narrow strips and make a crate. I have also make wall hangings and picture frames. Christmas ornaments, planter boxes, small furniture for kids or doll houses.... I am planning on building a medicine cabinet for my soon to be newly remodeled bathroom. With a few odds and ends the options are limitless.
Sorry got carried away. I might have other ideas, depending on what the dimensions are.