WOW! For it to melt that plastic, there has had to be a TON of exhaust gasses (CO) dumping into your house over an extended period of time . YIKES!
Years ago, I had a similar problem where mine was doing something similar but not to that degree. No melting. I noticed a cob web on the WH was blowing away from the exhaust hat so I looked into it. The old incense smoke trick showed me that it was flowing back out of the water heater vent. It took me a dumb minute to figure out what was happening but then again, it usually does - lol. My DWH exhausted into my chimney above where my boiler did. Originally it was fine but after the old boiler was upgraded to a power vented boiler, the boiler exhaust would blow straight into the chimney and basically pressurize it and push the hot gases out on the water heater like yours is doing. I corrected this by extending the boiler's steel exhaust pipe "up" inside the chimney, instead of just "into" it, and above the water heater entrance, which then created a sort of venturi effect and now, when the boiler runs it causes a vacuum/draft at the water heater.
Also, it matters what your exhaust pipe looks like outside....
Does it go above the peak of the building or at least have proper clearance so as to avoid downdrafts?
Like others have said, I'd definitely have a professional address that problem. Carbon monoxide and fire hazards are too serious to take lightly.
Best of luck on this.
