Are all these four expressions acceptable, what is the difference among them?
Among these, Sentences 1 and 4 are OK, but 2 and 3 are not.
Sentence 1 is a plain, matter-of-fact description ("I forgot something (e.g., in the room)."). Sentence 4 is correctly using both しまう and のです structures, and sounds as if you were explaining your previous statement, with the "regrettable" feeling.
A: Oh, no!
B: Hey, what's happened?
Sentence 2 is incorrect because the subsidiary verb しまう is following a noun rather than another verb. (Well, しまう can also be used as a normal verb, so actually this sentence could mean something like "It's because I stored the lost items (eg, in the shelf)!" But that's not what you want to say, is it?)
Sentence 3 is incorrect because する is followed by another する. Perhaps you wanted to write 忘れ物をしてしまいました, which is probably the most common and natural way of reporting things like this to your teacher/boss?