Your best option is to fork the project in github, remove the things you don't want, and then keep updating each with the new changes. With git, it's easy.
You may be able to remove the links and images (in the footer of our themes, and you could switch it on/off from the admin panel). You may remove the footer from the admin too, and even change the location of oc-admin to another folder but there are a lot of places that you will need to modify and probably will break your website. You need to change oc-content / oc-include folders, the update service, the market in the admin area, backups, ... some plugins and themes may stop working. It's a lot of work.