You will have to use JNI. No standard Java API right now provides you this sort of feature to query the event log. Win32 SDK provides all features for system access. The API to read event log is there. You need to use that API from your JNI code.
Its a 2 step process:
1. Writing Java interfaces which make use of events, event categories (Application, System, Error etc) exposed in Java
2. Interface methods mapped to native JNI mehotds (native methods to be implemented in C++ or C using Win 32 SDK)
To carry out these steps you may have to study :
1. How JNI works
2. The Win 32 SDK API for EventLog
* While programming for EventLogs, you wll find lots of other interesting APIS like Performance counters, Windows Registry,.... .. Its actually very tempting