The most topical cluster of meanings seems to be the financial ones: applied to companies, "experiencing financial difficulty or near bankruptcy", applied to assets, "offered for sale at a low price due to liquidation, insolvency, or foreclosure".
I had a vague idea that phrases like "distressed assets" and "distressed debt" stemmed from the 1980s junk bond era, so was surprised to find the word used in both these senses as long ago as the nineteenth century, in contexts that would not look too out of place in today's financial press. The Times in 1866 reported on tightening credit conditions, writing that the "leading banks..vehemently shut out even the smallest applications of any of the distressed companies for momentary assistance". The OED cites an 1899 article from The Chicago Tribune which commented (apparently in reference to some early bailout or aid for speculators fallen on hard times): "If the relief of distressed stock gamblers alone were contemplated nobody outside of Wall street [sic] would defend the proposition".
A comparatively modern usage is the fashion/design one - as in "distressed denim" or "distressed furniture". But again, it's not as modern as I assumed - the OED shows that it was in use as early as 1940 to refer to reproduction furniture made to look antique through "simulated marks of age and wear".
One sense which does not feel very current is the OED's note that the primary definition of "afflicted with pain or trouble" applies specifically to people living in reduced circumstances. This nuance seems to be disappearing - to refer to "distressed gentlefolk", or people living "in distressed circumstances" now has a quaint, old-fashioned air, evocative of Victorian philanthropy. Dogberry tells me that there is a sign on Greek Street in London (not London's Greek Street) offering aid to "ladies in distress", but I have never been able to find it.
A damsel in distress