Since then I have spent some time poring over manuals and trying some simple experiments, and I'd like to share what I have learned.
However, I am not an expert. No doubt I've gotten some things wrong. The only reason I am posting this material in the first place is that so little information on OO COBOL is available on the Web. If you want a quick overview without having to spend $50 on a book, or 50 hours deciphering a manual, then take a look -- but don't regard these pages as authoritative.
The version described here is IBM's implementation, mostly for mainframes, though I gather the OS/2 and AIX versions are similar. The draft standard evidently provides additional features which IBM has not implemented.
These pages will be best understood by those who are already familiar with the OO paradigm in general, and C++ in particular, as well as COBOL.
When to Use Object Orientation