Multiple delete in Microsoft Outlook Web Access

Did you try logging into your OWA with some other browser than Internet Explorer or Firefox ?

Opera for instance is not fully supported which can actually be a good thing since you don't get all that fancy Outlook imitation. The interface is much simpler and functionalities are much more available. You should then get a "check all" and be able to delete with increased speed.

Else, best solution would still probably to be able to configure and connect an Outlook client to your OWA...