"He acted expectedly" is correct, but is "He acted expected" also correct?
acted expectedly is correct, because acted is a verb, and you have to use an adverb to modify it.
The reason we can say He acted strange and He acted disorganized is because in this case strange and disorganized are actually describing the person, not the acting. These sentences can be viewed as short for He acted as if he's strange/disorganized. But you can't do this with expected because expected is not an adjective you can use to describe a person.