I've never heard of jGRASP before, but it is a Java application: this should not be difficult. If it's hard, then you are doing it wrong.
I went to http://www.jgrasp.org/ clicked on Download, clicked on jGRASP.zip, then in a terminal ran
Hey presto! It works, compiles and runs Hello.
I have these packages installed openjdk-7-jre, openjdk-7-jdk.
You don't need wine and you don't want to be trying to run jgrasp.exe under wine: that unnecessarily complicates matters.
$ echo $PATH
How did you install the JDK? Was it via one of the Ubuntu package managers? Can you successfully run javac from the command line?