Seriously; you can use an oyster card at croydon with no problems. you can buy and top-up one too.

Not sure about Croydon but if CW says so it must be so, seriously

But not all train stations (as opposed to Underground stations) have Oyster Card readers yet

such as at Eltham in Greewnich - even though they have Oyster looking readers i could not use my Oyster Card there even though the 'guard' at first said he did not know - the ticket window said no not yet. Apparently the readers were for some kind of SE trains pass?

They might be able to read travelcards on Oyster but not to communicate interactively with the computer for PAYG.

Good luck and have a great trip.