You're wrong here. The only way the nazis could have gotten away with their own law was if they could justify the holocaust as war related. Other than that, they had laws regarding stealing, kidnapping, and murder just like the rest of us. The difference was they didn't have a justice system that would enforce those laws.
Well, there is also the slight matter of crimes against humanity. The nuremburg and tokyo trials were really the first time they were used in court (the previous two being in the congress of Vienna of 1815 ending the slave trade and in WWI, when the allied powers denounced the actions of turkey against the armenians).
These laws were most certainly not on any one's books and were applied retro-actively to the beginning of the war. The courts were created not because of Germany's inability to prosecute the criminals, but because we wanted to. At any rate, Germany immediately after WWII was under complete political control of the allies (part of that whole unconditional surrender). So it's not like it wasn't capable of trying the criminals under its own legal system. It's that the allies "wanted blood".
What are the laws of germany from this period regarding kidnapping, murder, etc? Given that the concentration of jews and other "undesirables" was carried out in the open, it might be fair to say that german law did not recognize equality of the law to these people. If not, kidnapping, stealing, and murdering lower classes may not technically have been illegal in Germany. Admittedly, I do not know Germany's laws from this period.