Fast forward. Repeat weird emails that aren't from me. A couple friends alerted me and showed concern. I went to my settings to have a look. There was no suspicious activity in the logs Google provides. (Go to your Google+. Click on your avatar in the upper right corner. Click on Account, then Security. You'll see a box labeled RECENT ACTIVITY. Click VIEW ALL EVENTS. That shows you what you've done. If you see something you don't recognize, highlight it and you'll get more info to the right.) Also, my sent folder showed nothing out of the ordinary. A check of my apps (again under Google+>Accounts>Security>Account Permission) showed only Feedly had permission.
A possible culprit?
No, because after revoking access I'm still getting messages from concerned friends about hacking. There shouldn't be any way for someone to access my account without having my password. What's worse is I looked through Google's help for some kind of answer and found that Google is aware this is happening to people, but because it's outside their servers, they can't do anything but tag the emails as suspicious.
This is really annoying because my email is hooked up to Google+ which is hooked up to YouTube and that's where I uploaded the book trailers I made for people. But I don't want to hold onto an account that is spamming people. Somehow I have to hold onto Google+ and YouTube and get a new email address and deleted the one. Ugh!