Thanks all for your suggestions, but I found it!
As I said in a previous post, Malwarebytes, Avast, and AdwCleaner didn't find anything. Before going overboard trying this or that hunter program I gave Windows Defender a crack. It too found nothing. So either it's a program which isn't considered malware/virus, or it's something very obscure. And, because it was affecting both Opera and IE 11 it had to be a system wide something.
While letting defender to its thing, I surfed the web and saw several posts about hunter programs that would get rid of most unwanted. One of those posts suggested going to Control Panel --> Programs and features, and look for something that hadn't been on the computer before--several no goods were listed. I was about to grab one of those hunter programs from Bleeping Computers, when I remembered about looking at Programs and features. And sure enough, there it was, "Intelli Term 1.10.0.8", a program I didn't install but was on my computer.
Fortunately it had an uninstaller, because when I highlighted that program, hit uninstall, the uninstall wizard appeared and totally removed the program. I know it's worked because at the bottom of GB's post screen, where you submit your posts, the disable in "HTML is disabled" isn't highlighted.
So, here's another program to add to the
DO NOT ALLOW ON YOUR COMPUTER list:
Intelli Term 1.10.0.8Again, thank you all for the help you provided. Keep your eyes open.