Strictly any order. I'm serious. In principle, it's even possible to learn some of them in parallel. It could be confusing, but possible.
I would advise to lean C++ and C after C# and Java, not before, but some may disagree.
—SA
Updated 26-Jan-16 15:44pm
v2
If you have basic of C#, then it is very easy to learn C++, just syntax is difference but all concept are same. C is middle level language and it has bit different than C++/C# it contains Pointers concept.
I will categories languages as C at one side and C++, C#, Java at other side.
The sequence will be C, C++, C#, Java
I think "what you should do" is totally dependent on: who you want to be; what you enjoy, or have a 'passion' for; what specific goals you may have for the future in terms of employment, income, security, etc.
If your goal is to become a computer scientist; that's one path; if your goal is to become a creator of complex applications, perhaps on one major OS platform like Windows, that's another path; if your goal is to become a well-rounded programmer who can create complex web-sites, or web-apps, using back-end databases, multi-tasking, compelling user-interfaces ... another path. Becoming a game-programmer or multi-media programmer is, perhaps, another path. And, then there are numerous specialties, like device-driver writing, programmable-logic chip coding, etc.
Depending on your goals, mathematics, 3d graphics, in-depth mastery of one, or a few, computer languages, may have different priorities, and different choices of languages to emphasize.
Depending on your goals, studying very diverse computer languages from the point of understanding essential algorithms, and algorithmic complexity theory, may have first priority. Or, your goals may indicate in-depth study/practice in one programming language.
If your goal is employment within a relatively short period of time, that's another big possible influence/constraint.
I see (in your profile) you have experience in Clojure, and I think exposure to a Lisp-like language is a great benefit in helping you gain insight into other languages you will study.
So, as Microsoft asked in its 1996 ad-campaign: "where do you want to go today?" :)