The following tutorial details the process of how to turn on out of office auto-reply messages through the Office 365 Outlook Web App.
On the top right of the page, click on the Gear icon and then select Automatic Replies.
In the Automatic Replies window, select Send automatic replies then set the conditons of your messages. You can define the dates and times that automatic messages are sent as well as the types of contacts that receive replies.
*Note: If you don't specify a Start time and End time, you will need to revisit this page to manually turn off automatic replies.
Type your outgoing messages in the text boxes provided. You will be required to enter a message to senders inside your organization, but depending on your conditions in the previous step, you may not need to write a message to those outside your organization.
Click OK at the top of the page to save changes and the Automatic replies window will disappear.