Very likely, you have downloaded something from other than the original developer's website, and granted administrator privileges to install it. It probably contained a malware component that executes a Safari extension installer, as that is the only means to install an extension into current versions of Safari.
Starting with Safari quit, press and hold the shift key as you launch Safari. That will prevent it from reloading its previous application state. Do the following:
- Safari Preferences : Advanced : [√] Show develop menu in menu bar.
- Press option+command+e to clear your browser cache (and cookies)
- Safari Preferences : Extensions : Remove any extensions that are present
- Safari application menu : Clear History… [ all history ] [ Clear History button ]
- Quit Safari from its application menu
Download and install the free Malwarebytes for Mac, and run it. It is purposely designed to find adware/malware, and whether it flags anything or not, it may remove the source of your invading extensions. Quit Malwarebytes when it is done.
Launch Safari normally, and see if any extensions have returned. Remember, extensions get installed in Safari after an application is run that is designed to install them. What application did you download and install prior to your current Safari extensions mischief?