It could be an oil leak. Most cars of that age have some leaking seals and gaskets.
If you have significant drips of oil under the car after parking it (after driving it), then there's a very good chance the smell is oil vapors, which can form if the oil gets on a hot surface. Oil vapor can sometimes smell like plastic.
Maybe it "IS burning" plastic, -- or at least plastic that is real hot! Check under hood immediately after engine shut off, and check to see if anything hitting on exhaust mainfolds, or maybe engine block, - or water hoses. inside car see if smell coming from heating/cooling "registers" in passenger compartment, a heater motor going bad occasionally causes the "voltage dropping" resistor to overheat when running on slower speeds, - which in turn will transfer to "plenum" housing when fan not "moving air"! I have also seen "melting plastic occour with courtesy lights under dash, if the bulb is hitting on side of plastic mount/housing (when doors are open)! In short follow your nose - you will probably find it after a while by narrowing down what "isn't causing smell"!