Q:

Is there a philosophical term for an invalid argument based on extreme (and irrelevant) comparisons to Nazis? 

I use Nazis as a catch-all for any systemic atrocity that egregiously violates human rights.  I know the appeal is a false equivalence to Nazis and my argument.  However, I notice that often times when people get upset in an argument they end up proving Godwin's Law true (probability in discussion evoking comparisons to Nazis/Hitler approaches 1 as t -> infinity).  
Is there a term for the erroneous comparison or evocation of hyperbolic evil in an argument?  What labels are there for such fallacies?  

A:

Some texts call the fallacy of an appeal to a Nazi comparison to be "Reductio ad Hitlerum" or 'argumentum ad Hitlerum' (in this case 'Hitler' and 'Nazi' are synonymous or interchangeable).  
The nice thing about informal logic is that an argument made in a natural language often require us to paraphrase it so that it can be presented as an actual argument.  
Paraphrasing provides us with flexibility, and depending on how it is done, the argument could be guilty of a number of different fallacies.  
It could be a persuasive ad hominem when the argument is suggesting "You can't believe X, that's something a Nazi would say!"  
Appeals to Nazis could also be considered a faulty analogy, when the accusation takes the form: X is like what the Nazi's said/did therefore X is false/wrong (provided X isn't about mass-murder!)  
It can be considered a non-sequitur since it does not follow from the fact that Hitler believed X, that X is false.  Hitler (presumably) believed that Germany is a country, that the earth is round, that the sky is blue, that Pi is 3.14159, that the acceleration due to gravity is 9.8 m/(s^2), and many other facts.  These facts are not magically 'undone' because a monster recognized them to be true.     
The previous examples also show that such appeals to Nazi's are absurd, and thus we can also critique them via reductio ad absurdum.   
Finally these arguments can be construed to commit the association fallacy, or guilt by association.  
And those are just the ones I can think of off the top of my head.  The point is that you can stick with Reductio Ad Hitlerum but you have other options as well. 