What do you do about a major leak in a 2001 Plymouth Neon trunk and both back floors?

Check with the dealer to see if they will help.

Check the seal on the tail lights, mine was bad and it flooded the trunk and the back floor mats. You can use silicone sealant from a tube to seal the tail-lights without removing them. Open the trunk and also seal from where the top-inside of the tail-lights meet the plastic all the way up (several inches) to where this plastic meets the trunk body at a little rain duct. (you'll see it) Do not seal this duct. It may take more than one application around the lights to get a good seal. I live with Texas thunderstorms and haven't had a problem since.

Don't bother with the dealer unless your car is still under warranty. This problem is caused by the welding where the trunk meets up to the fender support and the cheap gasket around one of your tail lights. Gaskets can be replaced (expensively), but will only temporarily solve the problem. Above is correct about not sealing the channel where the water drains around the trunk, past the tail lights and down through the bumper. BUT, I removed my tail light (very easily done from inside the trunk). You will be able to see where the gasket has failed. Then you can put about a 1/4 inch bead of caulk around the entire gasket surface. Put the taillight back on, and the silicone caulk is your new seal. It should only take one application, but the caulk takes a day or so to completely cure before it can be rained on. $8 tube of caulk should be all you need. Now you just need to dry out your car, I would recommend peeling up the carpet partially as necessary and driving/parking with the windows open on days it won't rain.