Hmm, that is strange. You are correct with the x86 vs x64, Chrome / Firefox are only x86 AFAIK though you can get x64 nightly builds of Firefox. IE ships with x86 and x64, and I'd assume you'd need x86 and x64 plugins depending on which you'd choose.
Are you sure you have the Java plugin enabled on Firefox/Chrome (Not Javascript, these are totally separate)? Try checking your Java versions at
http://www.java.com/en/download/installed.jsp in each browser to see if they're registering the plugin on other sites excluding RuneScape.