I just updated to the latest Java version through System Preferences. I don't prefer any specific version. I see now that I have version 8 installed. I did figure out that I could run the Web Start version. My point is mostly that the error message is very unhelpful and I also didn't read anywhere that you have to use Java 6, or use 8 with web start. It would be helpful if that information was clearly shown somewhere during download/install/running. Also, I updated my Java version AFTER posting this...
Sweet Home 3D doesn't run on OS X Yosemite