Your examples aren't quite right.
And they aren't examples of quasi-complements, either. I should add that 'quasi-complement' is not standard grammatical terminology used by native English speakers.
'Quasi-complement' is an informal way of referring to certain phrases or clauses that, while not essential to the core meaning of a sentence, provide additional information about the subject or object. Your examples are just statements about two things happening at once. For example, someone humming as they walk - their humming isn't affecting their walking, or vice-versa.
That should be clearer as you see what is wrong, grammatically, with your examples. They all have the same problem - they either need punctuation to separate the clauses, or a conjunction to join them:
- He strolled, humming a song.
- He strolled while humming a song.
Subordinate clauses like "while humming a song" do not fit the quasi-complement category because they are dependent clauses that function to provide more context or detail about the action in the main clause.