Do you know which version of java and java3d you are using?

Try both and to launch from the command line. Does one of those work?

Check that SweetHome3D is using the included java runtime, and that it hasn't had a packager innocently trying to use the system installed version of java. (Depends on how SH3D was installed.) Examine the script, and check the PROGRAM_DIR variable is resolving to the included runtime java executable.