Which version of JDK did you install? Make sure it is the 64 bit version of the JDK otherwise it will not work. Also, did you have any other versions of JDK installed before trying to install Eclipse?
Also, why don't you try installing Eclipse with Intel's Integrated installer that can be found in Intel® Edison Downloads?
Does it make a difference?
Originally I installed via the "Integrated Installer" - or so I recall. I checked yesterday with a java -version command in the console window and confirmed it was 1.8.0_66, but now that command throws a "initialization of VM" error. I also tried double-clicking the "Java" icon that's in the Control Panel, but that does nothing.
What steps do you recommend?