I've been finding pages I've supposedly liked

For the last few weeks I have been seeing posts from pages and individuals (about 20 per day on average) that I have never been near, but that show I have liked them. I've laboriously gone through and unliked and even blocked them, but new batches keep popping up.
I see no other evidence of being hacked. No false friend requests going out in my name to my contacts and no attempts to take over my profile.
I've changed my password three times and still it's happening. I can't see how my profile is being used to add likes to these pages. Worse, there is no clear information in any Facebook support areas to help me. How is it being done? More importantly, how can I kill it off?