Most National Rail stations in the London area do not issue Oyster
cards, but a few do. Which stations are they?

In the TfL Fares leaflet there's a non-exhaustive list of NR stations
that *do* issue Oyster, but all these stations are either served by the
Underground/DLR, or have a NR route operating from them that accepts
Oyster Pre-Pay (e.g. Marylebone on Chiltern Railways, Essex Road on the
GN Electics route, Liverpool Street to Stratford by NR).

http://www.tfl.gov.uk/tfl/fares-tick...05.pdf#page=13

However I've heard that other NR stations (which are nowhere near the
Tube or any Pre-Pay NR routes) are now issuing Oyster, for example,
Surbiton. Is this true?

If so it would indicate that SWT were losing Travelcard sales to TfL
outlets, as passengers started to catch on to the benefits of having
their Travelcard loaded to an Oyster card. SWT, it seems, have
therefore decided to issue Oyster themselves, at some stations at
least, and win back those lost sales.