It was discovered that posts were initially set up allowing comments and pingbacks, which are a special type of comment created when you link to another blog post, as long as the other blog accepts pingback. This post walks through steps on how to turn off comments for old blog posts, but new posts will need to have the setting turned off. We will walk through the steps on how to turn off comments for new posts:

Click on Settings in left sidebar

Uncheck the box to the left of Allow people to submit comments on new posts and if desired, Allow link notifications from other blogs (pingbacks and trackbacks) on new posts.

Now the posts on your website should not have any comments going forward.