I've just taken a look at Google Maps (including zooming down to Street View level) and Google Earth.
It seems that you've not really got any choice about your route. The Travelodge is at the services off the roundabout where the A34 and A44 meet. Walking out of the slip road you can just follow round to your left, which will take you onto the A44 Woodstock Road towards the city centre. There's initially a footpath on the left, so you won't have to cross any roads by the roundabout.
Keep walking until, just a fairly short distance along the road, you come to a set of traffic lights (which is where the Pear Tree Park & Ride Facility is). Cross over to the other side of the dual carriageway at that point (because the footpath only continues on the right hand side).
Then, unfortunately, you come across the busy Wolverton roundabout. You'll have to cross the first road which is feeding in from your right (crossing two lanes to get to the central refuge, and then the single lane of traffic going in the other direction). Then you need to cross the next road feeding in from your right (which looks a lot quieter, with just one lane of traffic either side of a central refuge) before continuing round to walk down the right hand side of the main road into the city centre (which is still called Woodstock Road but is now the A4144).
That's the shortest route (3½ miles) and the only practical one.
However the Traveline website indicates that the Oxford Bus Company's Park & Ride buses (Service 300) are running on Boxing Day. The Stagecoach website states that there's also an hourly service on Boxing Day on route S3 between Woodstock and Oxford, which runs along Woodstock Road. The first bus should be at the Pear Tree Roundabout at roughly 0940 (with the last inbound bus being at about 1740). Buses leave the city centre (Gloucester Green, Bay 8) hourly from 0955 to 1755
On Christmas Day you could save yourself a bit of walking by turning left at the Wolverton Roundabout (along the A40). The next roundabout is the junction with the A4165 (Banbury Road), which will be served hourly towards the city centre by route N2. (I'd estimate that buses would reach the roundabout at a bit after half past the hour, from roughly 1030 to 1730). Return buses leave stop C1 on Magdalen Street hourly from 0955 to 1755.
Sources:
http://www.travelinesoutheast.org.uk
http://www.stagecoach...edetails.aspx?Id=1582
Chris