How should I add JAR libraries to a WAR project in Eclipse without facing java.lang.ClassNotFoundException or java.lang.NoClassDefFoundError?
Those JARs in the build path are referenced for the build (compile) process only. If you export your Web Application they are not included in the final WAR (give it a try).
If you need the JARs at runtime you must place them in WEB-INF/lib or the server classpath. Placing your JARs in the server classpath does only make sense if several WARs share a common code base and have the need to access shared objects (e.g. a Singleton).