Only the last one seems particularly unnatural, at least, in casual speech.
"What's the topic for the inside board for this month?" has that duplication of for which is a little awkward to me.
Assuming "the inside board" is a object that is well-understood by your class and the fact that its content changes every month is also well-understood, any of the first three would be OK, but you may need to pause slightly between certain words when you are saying them – a comma might indicate this in writing:
"What's the topic for the inside board, this month?"
"What's the inside board topic, this month?"
"What's the inside board topic, for this month?"
Be careful with the placement of the comma/pause, though—particularly with the third sentence—if you misplace it, another reader may take a different meaning:
- "What's the inside board topic for, this month?" could be interepreted as "Why is there an inside board, this month?"
To that end, I would favour the first sentence (with my comma before this month) in a written question; and the second sentence (where my comma is a slight pause) in a verbal question.