I would be in favour of upgrading Summertown to a suburb, given its prominence in local use and its own retail centre. 
North Oxford can be limited to the more central southern part.
Cutteslowe would remain a suburb (note that it extends to the south of the A40). Sunnymead should remain a lower tier, quarter is probably fine (nested, I am not sure, within Cutteslowe or Summertown, or both — city neighbourhoods are not and don't need to be always very precise).
The area between the railway/Woodstock Road and Banbury Road is a bit of a no man's land in my mind. I would say that (Upper) Wolvercote ends at the railway line. Wolvercote Cemetery is in Cutteslowe now. Not sure about the Blandford/Davenant/etc. part (it could be Sunnymead?).
Too early to say about Oxford North. The canal-side can be Wolvercote. The rest could be Peartree or its own small neighbourhood-tier place.

I am happy to sort out these edits, but I'd welcome points of views, given the uncertain nature of the matter.