Mechanism of Tear Gas (chloropicrin/Trichloro methane)
The general belief is that these agents are irritants which do not have a very specific effect.  That is to say that there is no specific cell or biological function that they set off, but that they irritate the cells, so the cells respond by putting up general defenses to insulate themselves from the noxious chemicals.  

Mucous and tears wash away the compounds.  I'm sure there are all sorts of things going on, but its hard to be more specific.  For instance, onions have many sulfhydryl (-SH) compounds,  many many of them.  In particular propanethial s-oxide causes the tears we get when we cut an onion. This compound is very reactive and reacts with all sorts of proteins and disrupts the membrane, etc.  Its perhaps an example of a specific irritant that is so reactive that it creates tears.  

An example of a specific reaction would perhaps be capsaicin.  There is a specific protein that is a heat receptor and the chemical capsaicin activates it, causing the feeling of heat/warmth.  

Tear gas and mustard gas appear to fall into the former category, which are chemicals so reactive that they just tear into the cell, damaging all sorts of things in there.