We are now required to replace Winsock with JAR/WAR distributable files as the way to send information from one server to the other server.
This is a very vague requirement. I suggest you clarify with those imposing the requirement what it means exactly.
JAR is a Java ARchive, WAR is a (Java) Web Application aRchive. They are means to distribute Java applications or libraries.
If you are using Winsock to communicate with a server now, why can't you continue doing that in the future? I guess the web application you are communicating with doesn't mind how web requests are generated as long as they conform to the API specification.
Java libraries can be compiled to native code on Windows and then used with Include/Declare statements from other Windows applications, such as your VBA code. - That might be an option use Java code on the client side.
As stated, clarify the requirements to identify more concrete questions.