Do traditional publishers always use offset printing for the books they publish, or do they sometimes use POD to make books available? If they do use POD, is it primarily for older titles?
Most traditional publishers now use POD for their backlists. It's a controversial practice, because some authors and publishers disagree about whether a POD title should be considered "in print" for purposes of determining whether rights revert to the author or not.
Yes, some of them use POD for their back-catalogue.
Bloomsbury Publishing has launched a digital global publisher, called Bloomsbury Reader, that will sell a back-catalogue of titles in e-book and print-on-demand format.
Bloomsbury Reader will sell books that have either never been printed before or haven't been available in print for many years. The range incorporates every genre including romance, children's stories, science fiction, politics, travel writing, biographies and poetry.
Print-on-demand as it affects conventional publishing agreements
Developments in cheap print-on-demand (POD) should make it easier to keep slow-selling titles available. This is good news; but it is prudent to consider safeguards. Works still available via POD might never go out of print, but the publisher might be sitting on a title which a new publisher would be happy to relaunch and promote along with its publication of your latest book.
Yes, small-press publishers use print-on-demand. It's hard to do a print run of less than 500 books more economically than print-on-demand, and many new books sell less than that.
In fact, by the time you factor in printing, shipping from printer to distributor, cost of warehousing, and shipping to retailer, it's sometimes really hard to do better than Amazon's Createspace. I was involved with one book project where doing a print run of 5,000 books only yielded an extra dollar of profit compared to having Createspace print the book, and the amount of work and hassle to get that extra dollar of profit wasn't worth it in the end.
They certainly don't do it traditionally, but Random House recently got some press for launching a POD service, so maybe it's on the way. They do say that it's more of a service for consumers than an expected money-maker.
Publishers may also use POD for production purposes (ARCs, etc.) - I'm not sure about this.