No, you can't use Oyster beyond the London fare zones.
For Cambridge if you travel from KIngs Cross (on Great Northern) or St Pancras (on Thameslink) you will pay £44.20 Anytime return during the morning peak.
After 0915 (St Pancras) or 0942 (Kings Cross) Off Peak Day Return starts at £30.30, valid on any return train. There are no advance fares on either of these routes, so you may as well pay on the day.
On the slightly slower Greater Anglia service from Liverpool Street you can get singe advance fares for around £13.50 from start of service, and throughout the day coming back. If you travel after 0928 there is a £23.50 walk up Off Peak day return fare.
To Oxford single advance fares on Great Western from Paddington are £6 each single in each direction from start of service.
These need to be booked several weeks in advance to get such good fares. In comparison a walk up anytime return is £77.30 or £31.80 off Peak day return from the 0920 train onwards.