As nouns the difference between postulate and law is that postulate is something assumed without proof as being self-evident or generally accepted, especially when used as a basis for an argument while law is (lb) the body of rules and standards issued by a government, or to be applied by courts and similar authorities or law can be (obsolete) a tumulus of stones.
As a verb postulate is to assume as a truthful or accurate premise or axiom, especially as a basis of an argument.
As an adjective postulate is postulated.
As an interjection law is (dated) an exclamation of mild surprise; lawks.