Yes it is possible to write a webserver in Java without any external (i.e. not Java SE) libraries. All you need to do is:
- Learn about
Socket
and ServerSocket
and the SSL stack, and ...
- Spend a few days reading the HTTP specification in sufficient detail to understand what the protocol requires.
- Spend a few more days implementing a server-side HTTP protocol stack and so on.
Which is ... a lot of effort, and probably a waste of you / your team's time.
If you are going to implement this in Java, you would be much better off either learning Spring / SpringMVC / SpringBoot, or learning Servlets and/or JSPs. They deal with the protocol side for you, and (more or less) leave you to focus on the aspects that are specific to your webapp.
These technologies (or equivalents) are what you are likely to use when you graduate.
If the other members of your team already know Java, that would be an obvious good reason to use it.
In short, there are 3 reasons to use Java + the above technologies:
- Less effort
- Less learning for your other team members1
- You / they will be learning more immediately useful things.
PHP would be another alternative, though if your teachers are "down" on Javascript for being "not OO enough", they are probably unlikely to think well of PHP either.
On the topic of whether Javascript is OO or not, read this:
Read it and make up your own mind.
1 - How about volunteering to write all of the project's documentation so that you don't have to learn Java. No? You want to learn Java, don't you!