Ok, the Oyster card works right across the London transport network.
Here's the map of all the rail and tube network covered by the Oyster card.
http://www.nationalrail.co.uk/passenger_services/maps/London_Rail_Tube_map.pdf
As you've discovered, Epsom station lies just outside the network: the very next stations (Ewell East and Ewell West# are inside Transport for London's zone 6.
However, London's buses -- also included in the Oyster system -- *do* run as far
as Epsom.
Assuming that your nearest station is Epsom itself, you will need to buy a Southern Railway season ticket. You can buy one which covers all London transport zones so it works just like an Oyster once you're into London.
It only costs a little more than a zone 1-6 Oyster travelcard. Compare the costs below.
Southern Railways London All Zones Travelcard from Epsom =
£58.30 (1-week card); £223.90 (1-month card)
Oyster Travelcard for zones 1-6 (out as far as Ewell East) =
£53.40 (1-week card); £205.10 (1-month card)
Hope that clears things up for you. =)