Can you sister floor joists with smaller boards?
Does adding a sister that is smaller than the original joist actually increase strength at all? 


Yes.  They will both bear the load.   


  If so, does it need to be sistered at the bottom (so both beams touch the sill) or does it still add strength if sistered to be flush on the top?


As long as the joists are attached together with sufficient strength, the force will be carried by both joists through the entire length of the span, but the larger joist will transfer all of the load to the sill.  That will work.  

Now if the joists are the same size, the attachment from joist to joist is not so critical - they can share the load from the floor without transferring part of that load from one to the other.    


  To extend the question, does a sistered joist that doesn't go the full span add strength? 


Yes, it will add some strength, although calculating just how much strength it will add may be difficult.