Iain wrote:

FOR EXAMPLE:
(1) Get on the tube at South Woodford (zone 4, Central line).
(2) Must travel via Stratford (zone 3).
(3) Get off at Ilford (zone 4, railway station served by One Rail).

Charged for one zone or two zones?

Neither, you'd get a penalty fare because Ilford is a Network Rail
station not served by the underground, and hence only supports Oyster
travelcards, not pre-pay.

You could rephrase your journey as South Woodford (Z4) - Stratford (Z3)
- change to Jubilee - West Ham (Z3) - change to District - Barking
(Z4) so that the whole Z4 - Z4 journey gets done on the tube, but I
think you'd get charged for the incursion into zone 3 nevertheless.

This is a bad example because you'd have to swipe your card at Straford to
get to the Jubilee Line from the rest of the station.

Although if you used the North London Line on the other side of the barriers
it might work. Does Oyster cover this one? And how can it tell?