Is there a utility similar to OllyDbg / SoftICE for java? I.e. execute class (from jar / with class path) and, without source code, show the disassembly of the intermediate
Take a look at JAD Decomplier for decompiling Java code. You can then run an IDE's built-in debugger using produced sources. IDE can be IntelliJ, Eclipse or NetBeans. This approach is not completely automatic, but it should do the job.