You can find out all emails received before or after a certain date with the Instant Search feature, and then then delete these found emails in Outlook. Please do as follows:

1. In the Mail view, type the search criteria received: <2016/1/1 into the Instant Search box, and then specify the search scope in the Scope group on the Search tab. See screenshot:

Notes:
(1) received: <2016/1/1 means search emails received before 2016/1/1.
(2) For searching emails received after 2016/1/1, please change the search criteria to received: >2016/1/1.
(3) For searching both emails received before 2016/1/1 and emails received after 2016/8/1, please change the search criteria to received: <2016/1/1 OR >2016/8/1.

2. Now all emails received before/after the certain date are found out and listed in the mail list. Select all search results, and press the Delete key to remove them.

Note: You can select all emails in the mail list with selecting any email and then pressing the Ctrl + A keys simultaneously.

Demo: Delete all emails before or after certain date with search criteria in Outlook

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.

Normally, Outlook users can sort all email messages by received date, and then select all emails received on or before/after the specified date, and batch delete them easily.

1. Click to open the mail folder that you will delete all emails before or after certain date from.

2. Turn off the Reading Pane with clicking View > Reading Pane > Off.

3. Sort all email messages by received date descending with clicking the column header of Received.

4. Select all email messages on or before/after the specified date, and then delete them with pressing the Delete key.
(1) For example you need to delete all email messages on or before 2014-5-1, see screen shot below. In our example, select the first email received on Fri 4/25/2014, and then press the Ctrl + Shift + End keys in a meanwhile to select all messages before the 2014-5-1, at last press the Delete key.
(2) If you need to delete all messages on or after 2014-5-1, you need to select the first email received on Mon 5/12/2014, and then press the Ctrl + Shift + Home keys to select all message received after 2014-5-1, at last delete them.

Demo: Delete all emails before or after certain date with sorting in Outlook

To delete all emails before or after certain date in Microsoft Outlook with the New Search Folder feature, you can do as following:

1. In the Mail view, select any folder of specified email account in the Navigation Pane, and click Folder > New Search Folder.

2. In the New Search Folder dialog box, click to highlight the Create a custom Search Folder, and then click the Choose button.

3. In the Custom Search Folder dialog box, enter a name for this new search folder in the Name box, and click the Criteria button.

4. In the Search Folder Criteria dialog box, click the Advanced tab, and then:
(1) Click the Field > All Mail fields > Received;
(2) Click the Condition box, and then select the on or before (or on or after as you need) from the drop down list;
(3) In the Value box, enter the certain date, such as 2014-1-1;
(4) Click the Add to List button.

5. Click all OK buttons to close all dialog boxes.

6. Click to select the new search folder in the Navigation Pane, press the Ctrl + A keys in a meantime to select all messages in this search folder, and then press the Delete key to delete these messages.

Demo: Delete all emails before or after certain date with search folder in Outlook