You will not be able to send any messages when your mail quota is full but you can still receive emails. Try the following ways to solve your problem:

A. Delete messages in your mailbox
You are advised to delete some messages (e.g. in Inbox) in your mailbox. Please follow these steps:

1. Click Inbox.
2. Select the messages you want to delete.
3. On the Edit menu, click Delete (or simply right click the selected messages and select Delete).

By doing the above, the 'deleted' items are only temporarily moved to the Deleted Items folder. Your mail quota will still be full if you do not delete these items permanently. To do that, follow these steps:

1. Click Deleted Items.
2. Select all (or some of) the items in the Deleted Items folder.
3. On the Edit menu, click Delete and say Yes when prompted.

B. Delete items in Journal Folder
The function of Journal in MS Outlook is used to record the details of the MS Office applications that have been run, and by default, this function is enabled. That means, when Outlook is running and if you open a file by MS Word, the access time and the file name will be kept in the Journal folder. Since the record is saved as a shortcut, you can just double click the shortcut icon if you need to open the same document later on. However, these shortcuts will also occupy a large amount of quota space as time goes by, and it may due to that your quota is full. To free space, you may delete items in the Journal folder by:

1. Choose Journal from the Go menu.
2. Select the items you want to delete. Choose Delete from the Edit menu and say Yes when prompted.
3. Delete these items from the Delete Items folder using the method mentioned in A.

You may also disable the default setting of the Journal function by:

1. Select Options from the Tools menu.
2. Click the Journal tab and uncheck the corresponding application check box in the Also record files from: window.

C. Move some messages to a Personal Folder
You may move some messages to a Personal Folder so as to free quota space. Check Question How do I back up my mail in Outlook? for details on how to create a Personal Folder, if you do not have one.