Stylistically is it acceptable to include equations and formulae in a literature review? I am writing a literature review as part of a master's thesis in mechanical engineering. 

I am discussing the approach of one author and I was wondering whether or not it is acceptable to include equations that the author has used?

For example I might say: Smith has used the ideal gas equation (and then write the equation) in order to calculate xyz...

This raises a further question in that should you include an equation if it is obscure, and omit commonly understood equations or not?
If the equation is important and not trivial knowledge (this can be debatable based on readership, especially in interdisciplinary work) there is nothing wrong with including it in a literature review (properly cited).
When in doubt, cite more than needed in the draft, as cutting down later will be easier than finding the reference again later.

The same goes for important illustrations/figures - for example of a reaction mechanism in chemistry.

Some people actively like to have equations or figures in the review as it provides a visual break in the text which can make reading easier.
Having said that, attitudes will differ based on subject field, country and just whoever reads it.