It usually depends in what CMS your website is written (like WordPress, Drupal etc ...). You could also ask your web hosting provider if they can help you with cleaning up your website.

Personally, I use a static website generator and I've never had any security problem. I can't give you any particular advice about how you can clean up your website, you could post a question on StackOverflow or do some Google searches once you know in what CMS your website is written.

(From your page source code it seems that you are using WordPress, do some research about cleaning up an infected WordPress site. The first thing that comes to mind is to always keep your WordPress updated to the latest version ... this, however, won't help you now.)