What's that tangy smell on cheap plastic? Most cheap items (from China mostly) have a strong tangy odor to the plastics (or some resin, but I can mostly smell it on plastics). The smell is always consistent over a broad range or products and I get it for at least a decade. So I do not believe this is a one-off thing and I bet most people have experienced it. The only variation is intensity.

On some really bad products that smell impregnates other things and I failed to remove it with soap, baking soda, acid, scrubbing...

I'm curious to know what exactly is that smell.

Apparently it got some attention already, but there's no consensus, and a lot of crywolf(?) e.g. Campaign to Halt the Import of 
Chemical-Emitting 
Smelly Plastic from China.
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