Which material sounds better for speakers construction? Wood, Ply or MDF?

I think it's close between ply and MDF. Construction matters however.
The best MDF I have seen use 1" thick layers to build up the case, with each layer using a different bracing topology. This yields an incredibly stiff and inert cabinet. but is very expensive and produces tons of dust.

Best left for those with access to CNC machines. Still, it's a lot cheaper than billet aluminum. :)

Best,
E

Try Magico they use aircraft grade aluminum as it sounds much better and is neutral.Mdf is history for state of the art speakers.

we made some speakers from   Bamboo 1 ply, 
the very solid material  ,and good acoustic performance 

There is no absolute.  
MDF is more dense than plywood or wood.  Wood on its own depending on type has all kinds of problems with expansion and contraction.  Plywood works, but still is a softer less dense material... However, if you are after an effect,  plywood can be more giving than MDF.. Also, the is no problem with gluing MDF & Plywood together, this works.  Way back when,  we built a cabinet out of concrete & ground up Styrofoam, worked great.  Also a few decades ago, I believe Definitive made some concrete enclosures.  

I built a pair of back-load horn single driver speakers last summer using the Madisound BK-16 kit design but modified it a bit and doubled up on the baltic birch side and top/bottom panels in the enclosure. The back panel and the front baffle were already double sheets. They came out great and sound real good with decent bottom end but took weeks to break in. I would have put some damping sheets between the panels but I learned about them after it was all done. May be next time. I may be old school or an amateur but I never warmed up to MDF except for shelving in my closet.