Here are the messes my kids have made where I've been totally at a loss for how to clean it up, clean it off, or remove it — and what finally worked.
(Now, I cannot guarantee that your kids aren't more creative than mine and will find messes to make that mine haven't discovered yet... but I doubt it.)
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Pencil on Walls or Painted Furniture — It sounds like you should just be able to erase it, but if you've ever tried that you know it ends up looking worse than before. You can use a Magic Eraser to remove drawing from walls (and pretty much everything from everywhere,) but it's gentler on paint to spray a paper towel with alcohol and wipe it off. You have to follow each pencil line and really scrub vigorously, but it works. The surface looks a little discolored if you leave the alcohol residue on it, so rinse with a damp paper towel afterward and dry.
Ink on Fabric — Put the inked area on a folded paper towel, spritz with hairspray and rub it in with an old toothbrush, then dab with another paper towel until it doesn't get any lighter. Scrub with Fels-Naptha soap (my all-time favorite stain remover) and rinse with cold water. I've done this with both black printer ink on white curtains and colored pen ink on a white shirt (why we even bother to have white anything in a house with 5 kids is beyond me) and it's worked great both times, even when straight-up bleach did nothing to reduce the stain.
Marker/Pen on Microfiber — Almost anything up to and including Sharpie marker comes right out of our microfiber sofa with rubbing alcohol and a paper towel. However, I have a love-hate relationship with microfiber. It's easy to clean, but it stains easily (even water stains it!) so no matter what, our cushions end up looking pretty gross after a few months. We zip the cushion covers off, wash and dry in the machine, and they look great. Ours haven't shrunk at all, but proceed with caution if you want to try it (i.e: no suing me for a new couch.)
Melted Candle Wax in the Carpet — Boil yourself a small pot of water and calm down. You can fix this. A little at a time, pour the boiling water on the wax to liquefy it and sop it up with paper towels. Repeat. Over and over. Then banish all candles from the house until your youngest child turns 18.
Crayon on Walls, Hardwood, and Tile — WD-40 is my best friend. Phillip keeps a can in his shop for something, but I probably use it way more than he does. If my kids draw on the walls or floors with crayon, I can wipe it right off with WD-40. I've also used it to remove artwork from a plastic toy and it worked great.
Pencil and Pen on Computer Monitors — I just about died the first time I walked in to see scribbles all over the computer monitor, thinking I'd have to trash the whole thing and sell my child on eBay (partly for punishment, partly to fund the purchase of a new monitor.) But it's super-easy to clean off with a paper towel and rubbing alcohol so I didn't need to worry.
Pee on Mattresses — Obviously this is one place where the best offense is a good defense, in the form of a waterproof mattress protector. But stuff happens and sometimes kids pee on the mattress. I've tried different ways to clean it out, but my favorite is this tutorial from Yellow Bliss Road. It calls for vinegar and baking soda.
...When All Else Fails — try Fels-Naptha. It's some kind of voodoo magic laundry soap, no kidding. Once my preschooler spilled an entire pitcher of red Crystal Light on a rug in our kitchen. I figured it was ruined but one bar of Fels-Naptha and some repeated scrubbing/rinsing in the bathtub later, I couldn't even see where the stain had been. That stuff is like fairy dust in bar form. There's nothing it can't take care of. I regularly use it both to make my own laundry soap and to pretreat even set-in stains before a load goes in the washer.
What about you? What are your most brilliant cleaning hacks for catastrophic messes?