So I've been having the same issue for quite a while. My Mac would be making error sounds when using Cmd-C, Cmd-Z, etc combinations. Rebooting would usually help, but it would usually start on its own after a while. I checked with this thread to see if anything would help, and nothing seemed to help, and I was legit panicking about viruses or something. I think I got the issue right after I updated my system (now have Mac OS X Sierra 10.12.5)
So I figured out today, that at least in my particular case, it's a bug with the Dock application. In fact, when clicking on Launchpad (show all apps) button on my Macbook, it wouldn't open (like open and close instantly). And when I opened it with a hand-gesture, I saw that everything I've been typing has been also typed into the search bar at the top of the Launchpad. Basically, the Launchpad (technically part of the Dock process) for some reason continued 'seeing' all of the keyboard inputs and would sound the error sound when I pressed a combination that wasn't appropriate, like Cmd-C.
Killing the dock process and having it restart fixed the problem instantly!