Well, finaly I did it. After installing everything I could imagine it might help and trying out all possible solutions I have Java plugin finally working in Iceweasel.
The solution was found on Java bug #4802695 first reported on 14-JAN-2003. The helpful comment #514 made by cava on 14-DEC-2008 said:
It works finally !!! Just need to link java-6-sun-1.6.0.12/jre/lib/amd64/libnpjp2.so in the Firefox plugins directory and we have it !!!!!!!!!!!!!!!!!!!
The command needed was:
ln -s /usr/lib/jvm/java-6-sun-1.6.0.12/jre/lib/amd64/libnpjp2.so ~/.mozilla/plugins/libjavaplugin.so