Luggage, Baggage, Suitcases. You can leave it somewhere safe and convenient…
There are many options is Oxford.
Radical Storage offers many options.
Radical Storage does not give precise details of the venue until booking but storage services are listed by location and they are rated so it is very useful.
There are also left luggage lockers at the Ashmolean Musuem, some big enough for all but the largest suitcase, but remember when the Ashmolean closes you will not be able to get to your locker.