@Beta_Orionis I don’t see why you can’t donate organs and be cremated? Also, I think you can donate multiple organs and be sewn back up and buried. I have heard some negative things about donating your whole body to science, something about a secondary market I think? I need to ask my sister, she is the one who warned me about it years ago.
I think @Dr_C makes a good point about direct organ donation. Jews believe that the body should go back to the earth, that it is part of the cycle of life. That is why they don’t embalm, and the casket should easily degrade. But, I think there is an argument for being able to give life by donating an organ. Some Rabbis are ok with certain organ donation.
Cremation would be a big no no in Judaism, because you are not able to nourish the earth. Moreover, since the holocaust, some Jews feel even more strongly about cremation, because the burning of Jewish bodies was done commonly by the Nazi’s.