That sounds scary, I hope you are all okay. Opening windows that day would have helped?
The only thing I can think of without calling a professional cleaning service would be a bit what others have said. Try removing some cold, but be careful around the heating element, not to break or crack it with too much pressure.
I was thinking at first some flame retardant material, but that would burn too, so you are better off with heavy duty foil, lots of it already torn off and wadded into amounts you can handle, kinda flat at one end to wipe up melted plastic. Have an old pan handy that you don't mind tossing out, or aluminum disposable pan. Must be something that won't melt, metal .. not glass. Then put on oven mitts. Then, put oven on absolute coolest setting.. 100 or 150.. however low you can go. Mine is digital and will go to 120. Get it *just* warm and turn the oven off. Then pick up a wad of foil and try to wipe the plastic up gently. Keep repeating. Be very careful not to get any molten plastic on you. To be on the safe side I would probably wear a paper mask too. If it doesn't melt at that temp, gradually go higher and be ready to turn the oven off and start scraping. If you heat the oven too high, the plastic will get too thin and melt down into crevices before you can wipe it up.
Years ago I put a plastic spatula in a skillet and set it in the oven. I put hot pans in there to cool before loading in the dishwasher. Well I forgot about it and preheated the oven. Oh man the smell... thankfully it just melted a little. I can't imagine how upset you must be.
Please be careful and let us know how it turns out. :)