For those of you having issues with your Facebook posting things you didn’t, and you use Facebook on a computer, I would advise you to run Avast Browser Clean-Up on your computer. It will scan for any add-ons in your browser(s) that could be using Facebook without your permission and remove them.
These unsolicited postings could also be caused by apps you’ve authorized on Facebook that you don’t use anymore or had a malicious intent when you signed into an app/website with Facebook. Go to your Facebook Settings > Apps and remove any Facebook applications you don’t use anymore, specifically those that have the ability to post content on your behalf, as those ones can like posts on your behalf.
A third culprit is websites that ask you to push the like button in order to see a video/content. In this case, pressing the like button could like something else instead on Facebook.
Also, it’s recommended that you change your Facebook password regularly. Use unique passwords for each website you login to. That way, if one website is hacked, and hackers are able to decrypt your password, they won’t be able to use it on any other site.
Stay safe out there.