What research gives insight into the terms "low status" and "high status"? Folk explanations of human behaviour often refer to "high status" or "low status", and the phrase sometimes pops up in more formal contexts (e.g. this question).

However, one of the most cited sources cited as exposition of these concepts is a popular book on improvisational theatre rather than a research publication.

What body of research, if any, addresses these concepts more rigorously?
This is a really broad question - what you seem to be asking is: what research addresses social hierarchies, competition, and neurological/psychological/physiological effects of perception of social status.

It's interesting to note that social status signals likely developed before language, as they are a means of non-verbal communication (language is quite new, evolutionarily-speaking).  

In the most broad sense, the answer to your question is that research on social psychology and social neuroscience, particularly that related to hierarchy, dominance, and perception of social standing, is what you're looking for.  This is the 'body of research'.

Past this point, I'm not sure what you're asking...  Are you wondering in what brain structures this type of behavior appears to originate?  Or are you more interested in the cognitive processing going on behind the scenes when people mentally alter their internalized social standing?  Or are you looking for a jumping off point?

If you are particularly looking for the neural basis of this behavior, check out the links below.  All relate to the neurological basis of social processing in the human brain.



Original answer:

I'm at work so I don't have a lot of time to put together a comprehensive answer, but here are some articles:  


Perigenual anterior cingulate morphology covaries
with perceived social standing  
Know Your Place: Neural Processing of Social Hierarchy in Humans  
The Cultural Neuroscience of Person Perception  
Using neuroimaging techniques to explore the relationship between social status and health
  
Neurobiological Correlates of Social Conformity and
Independence During Mental Rotation  
Neurobiological Pathways Linking Socioeconomic Position and Health



For the record, the Google search used to find these was neural correlates of perceived social +status