It is not necessary to reference very well- and generally-known results. For instance, it would be reasonable for somebody to say "by Pythagoras..." instead of trying to find a reference to his original writings ;-) I imagine that the Poisson Distribution would fall into the same category, but not being in your field can't comment on the others. Ultimately, as others have said, this judgement depends on your field and your intended audience. If in doubt, cite.
Re user manuals for software: If you have simply used the manual to learn how to use the software, a reference is not necessary - instead, reference the software itself. However, it would be appropriate to reference the manual if you are quoting from it, or if you are explaining how the software does a particular calculation and your evidence for this is that the manual says so (and perhaps provides more detail than you are including).