Wow, thanks for all the replies. Some of the information and links you guys offered will be very helpful to me in the future.

However, I feel a little silly, as I have been able to figure this one out.

Apparently (accidentally?) my "read receipt" settings got set to "automatic reply". Anyone sending me an email that had a "read receipt request" embedded was automatically generating the emails that have been going out. I have been able to confirm this through a few tests, and ultimately, finding and checking the settings for "read receipt requests".

I still think Outlook should leave a copy of the confirmation message in the Sent Items folder... this freaked me out a little, but I'm glad it was nothing.

Thanks again for all your help!!