'Chemical odor' is pretty general, but if the previous owner was trying to cover it up it's probably not a new problem. Odor from the black and grey tanks could be from a bad 'cheater vent' or toilet seal. Does the toilet bowl hold water? If so, one place eliminated. Your sinks most likely have 'cheater vents' which are used in place of actual roof top sewer venting. They are intended to be one way valves that often fail to close up again when water drains. They are screw on vents in cabinets under sinks.
Oatey 1-1/2 in. ABS PTC In-Line Cheater Vent-39012 - The Home Depot
Also, if you have plumbing for a washer/dryer, that trap can be dried out and cause odors. You might use a cap on the stand pipe if you don't use it.
Check for signs of roof leaks that might be causing mildew or mold in ceiling or side walls. Sniff the walls, carpets, etc. for signs of mold or rot.
I'd ask local shops for advice about steam cleaning the ceiling, it might cause drooping in a fabric cover 18 years old by destroying the adhesive holding the fabric to the padding or stretching the fabric.