I used to think you needed 32-Bit for 32-Bit programs and 64-Bit for 64-Bit programs.
Later I found out this wasn't the case even though at the time, and still to this day, java.com's download button gives you an installer for 32-Bit Java.
JAVA_HOME should be your JDK location
PATH should contain your JRE location (JDK has a JRE in its bin/ folder) as one if its elements
Note that manually specifying the path to the java executable is possible,
and after changing any variables you must restart the programs that need them
I know he hosts his mods on his own website, but I see you have one of his mods that I can't find on his site and that is the one that is out dated and has a suspicious name
I'm afraid the amount of coremods installed makes it difficult to determine who's at fault, if it's even possible to do so.
Please provide your debug.log as described in the EAQ and the logs section of my signature below and I'll see if I can give you any more information.
Note that this may not be possible due the aforementioned amount of coremods.