Vinylic polymers often have monomer (vinyl chloride) residue and additives(organic phosphates, organic/inorganic dyes, aromatic hydrocarbon-derivative flame retardants and other stuff.) When properly polymerized, monomer residue is negligible. Good quality additives require small concentrations to make their effect. Therefore, a good vinylic plastic has little if any monomer residue and just enough additives. Whatever remmant of both quickly evaporates and the concentrations are too low to pose a health hazard
Needless to say, most of this additives are petroleum products. Refined petroleum derivatives are converted into monomers and additives using carefully developed (and tightly held) processes that reduce waste and yield quality products with high purity.
As far as I know, the Chinese chemical industry lags behind its Western counterpart and its finished products are often below the necessary concentration or degree of polymerization. Therefore, there is some monomer left and more additives are needed to prepare the final product, be it a calculator case or an appliance housing. The excess quantity has to go somewhere, in this case the air, and an undesirable odor resulting from monomer and additives is the result. The unavoidable price of using cheap materials which in turn come from rather poor manufacturing processes.
There is not much to do about this except washing the case and let it in the open for a while until all the excess chemicals evaporate. However, it might take a while, and it is better to keep it away.
Your headache may be either the result of an allergic reaction or symptoms of exposition to a monomer/additive mix level that exceeds your tolerance. So it is safe for you to keep the case away.
My two cents.