All of your sentences are correct, but as you guessed, each conveys a slightly different order of events, as well as a different feeling.
As you describe them, this is an action scene, and it would be most natural to describe the events simply, in order not to break up the action, for which the simple present participle works nicely:
Without warning, the old man turned and hit Johnson square in the face. Staggering back, Johnson sank to the ground. "What'd ya go and do that for?" he cried, holding his red and bloody nose.
"Having staggered back" breaks up the action by separating the staggering from the sinking, which indicates one may not be the result of the other.
Wilson clutched his chest in mock horror. Having staggered back from the terrible scene of the young men drinking white wine from what were clearly claret glasses, he slowly sank to the ground. "You lot really are nothing but a bunch of uncouth apes," he sighed.
"After he had staggered" again separates one action from the other, slightly more so than "having staggered back". I would probably not use the perfect tense, though, as the simple past is fine:
Looking behind him, Wu didn't see the door opening and, as he turned, he walked right into it, face-first. After he staggered back a few steps to catch his balance, he sank to the ground, touching his face gingerly to see if anything was out of place.