<p>What is the difference between these three heavily related fields? Is there one specific whole they are all a part of (aside from CS)?</p>

Machine Learning
could
be considered a part of AI, however I would classify Machine Learning as the study of creation of semantic models and adaptive behavior with AI being the overall science of systems that intelligent-seeming behavior.
Most of what goes as "AI" is rather simplistic, but highly effective, such as heuristics and the like.
Soft Computing doesn't fell like it has many ML and AI components as it is more about analysis of complex systems.  I could be wrong though.  As with most things in computer science, the deeper you dig, the more you discover that it's all related.