You can permanently delete email messages from the Inbox folder easily.

1. Open the Inbox folder, select to highlight the email messages in the Inbox folder that you will delete permanently, and press the Shift + Delete keys at the same time.

2. In a pop-up warning dialog box, click the Yes button. Then all selected email messages in the Inbox folder are deleted permanently.

Note:
(1) This method can also be used to permanently delete email messages from other folders, such as Sent Items folder, Drafts folder, Outbox folder, etc.
(2) Holding the Shift key, you can select multiple adjacent email messages with clicking the first email message and the last one.
(3) Holding the Ctrl key, you can select multiple nonadjacent email messages with clicking each one separately.

Quickly Search and delete duplicate emails in Outlook

With Kutools for Outlook’s Duplicate Emails feature, you can quickly find and delete them from multiple mail folders, or find and delete all duplicates from the selected ones with two clicks in Outlook.

This method will guide you to archive old emails from the Inbox folder with the AutoArchive feature, which can permanently delete old emails automatically.

1. On the Navigation Pane, right click the Inbox folder, and select Properties from the context menu. See screenshot:

2. In the opening Inbox Properties dialog box, go to the AutoArchive tab, and do as follows: (1) Check the Archive this folder using these settings option; (2) Define the old email as you need, such as 3 months; (3) Check the Permanently delete old items option.

3. Click the OK button to save the settings.
From now on, it will automatically and permanently delete emails/items older than the defined time period from the Inbox folder.

Note: This method can also automatically and permanently delete old emails/items from other folders, such as Sent Items folder, Calendar folders, etc.

If you have deleted many email messages before, you can permanently remove these deleted email messages from the Delete Items folder quickly.

1. In the Navigation pane, right click the Delete Items folder, and click the Empty Folder in the right-clicking menu.

2. A warning dialog box comes out. Just click the Yes button to exit this dialog box.

Then all deleted email messages are permanently removed from the Microsoft Outlook at once.

Note: If the Deleted items folder includes subfolders, after clicking Yes button in the warning dialog box, all items in the Deleted items folder will be removed including the subfolders.

There is an alternative method to permanently remove all deleted items from Microsoft Outlook immediately. You can do it as following:

1. Open the Mailbox Cleanup dialog box:
A. If you are using Outlook 2007, please click the Tools > Empty "Delete Items" Folder.
B. If you are using Outlook 2010 or later versions, please click the File > Info > Cleanup Tools > Empty Delete Items Folder.

2. In the pop-up warning dialog box, just click the Yes button to close it.

Then everything in the Delete items folder will be permanently removed in a minute. 

Note: If the Deleted items folder includes subfolders, after clicking Yes button in the warning dialog box, all items in the Deleted items folder will be removed including the subfolders.