1 means he started high on the staircase , and fell down ALONG THE LINE OF THE STAIRCASE, hitting all or several of the lower stairs on the way down. 2 and 3 mean he fell OFF THE SIDE of the staircase, and fell vertically to the ground.

He fell down the stairs = he hit several stairs on the way down He fell down from the stairs = he did not hit any stairs on the way down, maybe there was no banister He fell down from the stairs = He fell from the stairs, down usually understood because cannot fall up from the stairs usually understood to somewhere else He fell down off the stairs = he fell off the stairs = complete action, no "to" understood Let's use jump He jumped down the stairs - jumping down several stairs to the bottom of the stairs He jumped down from the stairs - to the bottom of the stairs He jumped from the stairs, could be jump up to someplace else or down to someplace else, not jumping on any other stairs he jumped off the stairs - complete action, don't know to where