None of your needs are particularly complex, and almost any language would meet them.
Given the short time-frame and the fact that your grades depend on submitting a suitable application I'd suggest that unless you're really driven by the idea of learning something new you should stick with a language you already know -- and given the choice between Java or C I would probably suggest Java, although obviously if you have a preference for C you should stick with it.
It's not clear from the description whether you actually need to make a playable game or if you simply need to create an application which connects to the server and sends commands to control an AI tank. I assume you'll probably also want to display what is happening?
Your first move should probably be to put together a basic application that is able to connect to the server and display the information it is given. You can then build from there to send commands back to the server -- start by just naively sending them with no decision-making to confirm correct functionality -- and then work up to actually making intelligent decisions based upon the situation at hand.
You should also focus on whichever part of the application is most important for the assessment: if it's mostly about testing your ability to implement networking capabilities you should focus your efforts on creating a robust networking solution and just have a simple AI player to demonstrate those capabilities. If the AI is the focus you should just get some basic sufficient networking functionality implemented and then focus on creating the best AI possible. If you have time left over once the most important feature is satisfactory you can then proceed to improve other areas, but don't waste your effort on things that aren't important to the assignment.
You've said you're experienced with Java and C, but have you created
games with either of those languages?
If you really want a different language my recommendation would probably be
Python, but just to reiterate I would really suggest sticking with what you already know unless you
really want to learn something new.
Hope that's helpful!