I have been getting a few Mail Delivery System emails with the subject header "Delivery status notification" the emails say:

This is an automatically generated Delivery Status Notification.

Delivery to the following recipients was aborted after 0 second(s):

then some obscure email address.

First I thought it was a virus and my system was sending out emails to bogus people and some system was returning it to me, I did a scan and fixed a couple of minor things and kind of forgot about it....but when I left town I had turned my machine off for a long while (at least a week) and while away checked my email from time to time on my cell phone. I was still getting these messages daily.

Oh, BTW the emails have attachments but Outlook has blocked them because they are deemed unsafe.
What do you think is going on?

a computer bot scanned your email

or some company sold your email addy

change over to Gmail free and you can filter the message out
selecting the do not send to spam, delete it

you can leave your present email intact and forward or import
your mail to gmail

Someone (spammer) is spoofing your email address and you are getting the rejection notices.