How to fix SEO spam injections

Recently we noticed several SEO spam injections on the same pattern, starting with a list of encoded malicious files.
If you notice any of these inside your root folder, it means your site is infected: auto_seo.php, accesson.php, wikindex.php, old-index.php, 3index.php. Moreover, any addon sites, hosted on the same account, will be affected by cross-site contamination.