Much depends on whether you plan to spend time going to other places from Edinburgh as to whether or not you should cut a day. Here is a tour operator from Edinburgh. You might like to consider the places you could go to from this city:>https://www.rabbies.com/en/scotland-tours/from-edinburgh
Regarding stopping off at Durham: the cheapest train tickets for longer journeys are advance singles - ideally purchased about 11 weeks for the lowest prices. If you purchase advance tickets for a specific train, you are not allowed a break of journey, so you would have to buy split tickets. I have not been to Durham but I understand that it is steep so could be a problem lugging cases with you.
Be careful when choosing accommodation in Oxford as you could find that it does not come with parking. Click the link and you will get a map of Oxford - the rail station is marked by the red symbol.https://www.google.co.uk/maps/@51.7524171,-1.2708904,2944m/data=!3m1!1e3!5m1!1e1
You may like to consider getting off the train in Oxford and have a hire car company pick you up/or/ taxi to their place. Then, head for an out of town place such as:>https://www.travelodge.co.uk/hotels/80/Burford-Cotswolds-hotel
(Burford in one of the nearest Cotswold villages to Oxford).
Use one of the many hotel search sites to find out what is right for you and your price range.
(Around Oxford you will see Park & Ride (P&R). This means that you drive to a car park on the periphery and shuttle buses will take you into the ancient middle - where traffic is banned from many streets.https://www.oxfordshire.gov.uk/cms/public-site/park-and-ride