What's that tangy smell on cheap plastic?
Without a sample and a gaschromatograph it is hard to say what exactly it can be but... there are at least three well-known sources of odour in plastics:


Some residual of the monomer that makes up the plastic (that is a polymer).
Some residual of some other substance used during the manufatcturing process (catalyzer, co-polymers, modifiers and so on). For example, PETcan sometime contain small traces of terephthalic acid.
Some odourizing substance that is added to the plastic just to cover others smells.


Usually, tangy smells are a symptom of some kind of  ester