I'm currently working (almost finishing) a Java project that consists on a server application and some client applications on the same network, that will communicate with the server only to request informations. So what tools are suggested to use for this kind of testing?
Try Jmeter to test performance of your app.
If you are looking for automated UI testing using java then Selenium is worth having a look at....
SoapUI is a nice tool to test (not only SOAP!) webservices, define several types of assertions on the responses, build functional tests and also derive load tests from functional tests.
As a (super nice) plus, mostly everything in SoapUI can be scripted with Groovy, which allows for even more flexible testing, and finally, there is also a Maven-Plugin which lets you integrate all your tests easily in a continuous integration/testing/deployment scenario.
As you wrote in the comment your are mainly looking for performance testing and functional testing,
For performance testing I would recommend you user Jmeter. It is a java based tool so it should work really fine and for web applications I would suggest you record your test scripts using Blazemeter (an extension of Google Chrome). Here is a tutorial to help you with it - http://testacy.co.in/performance-testing-jmeter/
For functional testing I would suggest you to use Selenium Webdriver and if you are familiar with the TestNG framework of Webdriver that would be more preferable. Since Selenium is open source project you will get a lot of help from countless blogs and forums dedicated to it.
Though JUnit helps in writing unit test cases for java code, it will not be able to help you to speed up the testing process with increasing numbers of test cases to be executed and more data to be processed.
Jthunder is a core automation framework which helps in enabling multi-threaded processing of any JUnit tests/Java code.
Have a look at the Jthunder framework documentation.
As you are looking for tools for functional testing of your application, I can recommend Ranorex. It is a powerful tool for testing the UI of your application automatically. At the end of every test run an XML based report is generated, containing screenshots if anything went wrong.