All three have frequent (and often semantically half-empty) use as intensifiers or hyperbolic helpers.
In actual truth means "In real truth" and underscores the truth of this truth, as contrasted with the untruth of the "truth" you've heard before. Actually, like really, seems to try to dispel doubts as yet unexpressed. In actuality means "Here's what really happened." All three words have useful literal senses too, but care is required to evoke them.
Kenneth G. Wilson (1923-). The Columbia Guide to Standard American English. 1993.