Like Integral, I am not familiar with the term 'physical cosmology'.
The other three terms (astronomy, astrophysics, cosmology) have different meanings in different contexts, and on top of that their meanings have changed over time, even within the relevant scientific communities! A good example might be how the study of the inter-planetary medium (IPM) and solid solar system bodies has changed over the past century or two: today, the former is largely the domain of 'space physics', or 'space science' (the study of planetary magnetospheres is included here too), whereas it used to be exclusively part of 'astronomy'. The huge change came about because we can now study the IPM (and magnetospheres) with in situ space probes such as http://sci.esa.int/science-e/www/area/index.cfm?fareaid=8" .
Today 'astronomy' tends to be used for the observational aspects - the data from the instruments attached to telescopes1, the design of such instruments, the design of surveys to be conducted by them, and so on.
'Astrophysics' tends to refer to analyses and interpretation of the data gathered by astronomical equipment, by application of physics theories, models, and hypotheses formulated using such theories. Some parts of astrophysics could, perhaps, be more logically called 'astrochemistry' (or similar), because the theories used are drawn more from chemistry than physics. 'Astrophysics' can also refer to the flip-side - descriptions of phenomena that could be observed by (only) astronomers, based on developing physics theories, models, and hypotheses and applying them to 'the real world'.
'Cosmology', as a science (not to be confused with any purely philosophical connotations), addresses questions about the universe as a whole - how it evolved, what physical mechanisms are responsible for that evolution, and so on. In one sense, cosmology is 'just' a part of astrophysics, as it addresses only a sub-set of the phenomena (and physics) within astrophysics' domain; in another sense it's the other way round - in principle, everything in astrophysics should be derivable (if there is such a word) from cosmology.
In the last twenty years or so the term 'observational cosmology' (perhaps this is what you meant by 'physical cosmology'?) has become common. In one sense, this is just a branch of astronomy, concerned with observations which can (or might) be used to test cosmological theories, models, and hypotheses.
1 Of course, many 'telescopes' have little resemblance to an amateur astronomer's Newtonian reflector![/size]