Select File>Tools>Mailbox Cleanup.

Once selected, that will open the following prompt.

We recommend selecting the radio button next to Find items larger than and entering 9999 kilobytes. You may need to expand the window to see the size column. This will then filter on all of the messages in your folders that are over 10MB. Select Find. 

 It will then display your Inbox with the search criteria and you can go through the results and delete any unnecessary emails to help clear up space.

Alternatively, within the initial prompt, you can choose View Mailbox Size... as another way to look through your inbox folders to determine where the most space is being used.

Make sure to choose the Server Data tab as that is where the storage is limited. 

Once you have cleaned up your mailbox, you need to go into your Deleted Items folder in Outlook and delete the contents or they will continue to take up space in the server as shown above. 

Please use caution when cleaning up your deleted items as this will permanently delete the message. 

There is an option to delete all contents in your Deleted Items folder. Right click on the folder and select Empty Folder.