The Bodleian Libraries website explains who can access which online library resources: https://www.bodleian.ox.ac.uk/services/remote-access
In general:
University members
Those attached to a college, department, or institution of the University of Oxford, as a member of staff, a student, or an academic visitor, with a blue University Card
University members may access e-resources both on campus and off campus. To access e-resources off campus, University members must sign into SOLO using their Single Sign On (SSO).
Bodleian Readers
Those with gold, silver, mauve, green or red Bodleian reader cards
Those with a Bodleian reader card may access e-resources when on campus using a computer in a Bodleian Libraries reading room or their personal device. If using a personal device you will need to be connected to the Bodleian Libraries WiFi network and to SOLO. You will not be able to access e-resources remotely when off campus.
Alumni
Alumni of the University of Oxford can access a number of online library resources on or off campus after registering for the service: www.alumni.ox.ac.uk/journals