I understand that Struts 1 is EOL but I would like to know if a project that uses Struts 1 can work with Java EE7 or do I have to stop using Struts or start using Struts 2
I don't seem to find any documentation of that matter.
Struts only uses Servlet API from the EE implementation. As far as I know it's designed to be backward compatible with other servlet specifications. But you can try it on your own risk, because it might not be built or tested under the new specs. The best approach is to build the framework yourself to see if you have any problems with it. On the docs site (which included with the distro and no longer available online) and on Maven site you can find which Servlet API was supported, this information is also in release notes.
You can use old Struts as I already said on your own risk, means this framework is no longer supported. If you need a support from the community then you should upgrade to Struts 2.