There's usually room above Isis Lock if you don't arrive late. Be careful coming in if you try any of the moorings further up in Oxford, some are shallow or have bits of bank that have fallen in to cause obstruction even if they're signed as 7 or 14 day.
On the Thames, assuming a short term license (there are EA patrol boats) East Street below Osney bridge is good for one night. From a few hundred m below Osney lock to Folly bridge there are a few places to moor but unattractive and no meaningful time limit. There are always boats tied up opposite the entrance to Osney Mill marina which is bloody annoying as they make it hard to get out of (I moor there). It's usually feasible to find a space opposite Christchurch Meadow if you don't mind a bit of a walk back to the bridge. My favourite spot though is upstream from the end of Sheepcote channel. Plenty of trees to tie to, usually plenty of space, quiet (the bottom end of the canal can be very noisy with trains), not much used and only a few minutes walk to town. In theory 24 h limit but you'll struggle to find the sign.
Martin/