Another vote for Goo Gone. That stuff is awesome. I used to work in a library and we used it all the time to remove tape residue from shelves, desks, etc, and labels. It works great, but sometimes you need to just let it sit for a while before you wipe it off. In addition, it is also good at removing crayon from white boards (dry erase boards) and probably from other surfaces as well.
If it's a really sturdy vinyl, you could make a tote or messenger bag from it. I've never done it, but I've seen photos of bags made from billboard vinyl which seem pretty cool. I have made bags from the heavy plastic bags that some pet foods and bird seed comes in. If you have a sturdy needle and use a roller foot (or maybe a teflon foot or a walking foot if you have one) you shouldn't have much trouble stitching it.
When my son was learning to use the potty, we used an empty wipes container as a potty for some of his stuffed animals. When you open the lid, the hole in the top looks vaguely like a toilet seat. We would put Duck or Lamby on the potty and cheer like crazy at their potty success.
Also if you enlarge the hole so it's big enough that your child can reach a hand inside without getting stuck, you can use the container to play a guessing game with your child once he starts talking. You put a small object inside and have the child reach inside (without peaking) to feel the item and try to guess what it is.
My 3 year old son would want to live with you. He loves to play birthday party, in which we have a party for one of his stuffed animals, complete with pretend food and presents. He chooses random toys for us to wrap, but I refuse to use new wrapping paper or tape so we reuse old wrapping paper as well as some really worn brown paper that was originally packing material. I use and reuse pieces of yarn and curling ribbon salvaged from old balloons to tie up the packages. And even aside from playing with it, your paper could make a neat distressed-looking wrapping paper, assuming the pieces are big enough. It is probably sort of rumpled already, so just crumple it up and then smooth it out again. Wrap up your package and tie it with twine for a rustic look.
As for the boxes, if you don't have kids who love to play with them, some might be the right size for storing magazines or files. I recently read a book where they sewed a fabric slipcover to cover a box and it actually didn't look cheesy. And if you are in need of furniture, you can find instructions for making your own chairs and tables from corrugated cardboard.
If you give wine as a gift, you could use your fabric samples to stitch up simple wine bottle bags and tie them up with coordinating ribbon or twine. You could also use the bags for other gifts like jar candles, perfumes, or anything else you could fit in them. One year I stitched up a whole bunch of these bags, included a bunch of coordinating ribbons, and gave them as a gift to a friend who was always spending way too much money on gift bags she bought at the last minute. She got a lot of use out of them. Alternatively, you could make cute little tote bags with them.
You can do something similar with a small piece of ribbon or thin elastic. I have a pair of jeans whose zipper just kept slipping down. I cut a bit of thin elastic (that came on a pair of new kids' shoes; for some reason they were tied together with a long piece of very thin elastic) and tied it in a loop through the hole in the zipper. I just zip up, hook the elastic over the button, then button the waistband. It works great.
If the plastic doesn't have a sharp edge when you cut it, you could make some toys for kids to play with in the sand or water. If you cut off the bottom, the bottle could be used for a scoop with the cap on or a funnel with the cap off. Also, you can use a nail or a pushpin to poke holes in the bottle cap so you can use the bottle as a watering can. You can cut off the top part of the bottle so kids can use the bottom as a sand mold. And you could cut off the top, poke holes in two opposite sides to attach a string or ribbon for a handle and let the kids use it as a bucket for transporting sand or carrying little treasures they pick up on a walk.
Check your bookstore, or better yet, your public library, for books on recycling or remaking or altering clothing. You may be able to convert a too-small-in-the-bust pullover to a cardigan which you could wear open. Or you could take a sweater apart and use the pieces to make scarves, hats or mittens (especially wool sweaters, which you can felt first in your washer at home). I am sure someone on craftster or instructables has probably done some inspirational thing that will appeal to you! And if the sweaters are just a bit too small and made of natural fibers, maybe you could block them to stretch them a tiny bit. I don't know if your dry cleaner could do this for you, but it wouldn't hurt to ask.