How can I accept several meeting invitations at once in Microsoft Outlook 2013?
There is no way built into the Outlook 2013 standard interface to accept multiple discrete invitations simultaneously.
There is Automatic Accept or Decline, found in File > Options > Calendar which will accept every invitation that does not conflict with an existing calendar event.
There are Macros which could be written to accomplish this in some form.
And there is a toggle that activates Send Response Now mode that is normally hidden from the UI but that can be made visible and available using this answer here: Single click to accept meeting invite in Outlook 2010
Note, that answer is specifically for Office 2010. In Office 2016 the name has been changed or is no longer a valid command. I do not have Office 2013 handy to see if it it available there.