wood glue is the best thing for gluing wood. ill explain how the bonding process works, relative to mdf.
first, here is the thing i have never seen anyone do correctly. mdf has a layer of sealer on it. for best result, you have sand through the layer of sealer to get to the actual wood, to get the best bond possible. wood glue is thinner than liquid nail. i mix my glue with a lil bit of water to make it even thinner, because if the glue is thin it will soak into the material for a very strong bond. with liquid nail, it is so thick that it doesnt soak into the wood, and all you get is a surface bond, with is the structural equivalent to having a battery with a dead cell. sure it shows voltage, but put some load on it and you aint got shit.