Επιχείρηση can mean either 1) a military plan or the organized effort to achieve a goal 2)the business= εταιρία. So, it is now added as an alternative. The difference between them (apart from the 1st meaning that εταιρία does not have), is the same difference as business and company.
Ah - hadn't come across πολυεθνική. But I'm not sure in English whether there is any distinction, except that multinational is (in the UK) probably the more common usage. If there is a distinction, a multinational should be bigger, because you can be international by operating in two countries, multinational requires more. There is also supranational which implies that the company is truly global without and national base, altho some economists dispute that any such companies exist.