"Sleeping on a chair" is perfectly fine English. My cat sleeps on a chair in my house regularly. He doesn't sleep in it. Size and comparatives are at play here, and whether or not the chair surrounds or envelops the subject. "In" and "on" are both as common as each other in this type of sentence. Anyone who states that "on" is incorrect should be ignored.
That order doesn't sound right to me with either preposition... it separates the action.
He is in/on a chair = Ele é em uma cadeira
He is sleeping = Ele esta dormindo
If you say "He is in/on a chair sleeping" you start to think of the sentence like "Ele é em uma cadeira" and then tacking the action on to the end is jarring. (For me at least).