If the wooden core is laminated vertically in strips it increases the likelihood that it will behave more consistently as the variations in the grain are sort of averaged out by the combination of many different wood strips. Tua skis are made this way. Some manufacturers opt for high-density foam cores that are not injected but ground to shape. Don't confuse this with the old low-density injected foam cores. They'll argue that they can control the properties of the foam more precisely than wood by altering the chemical composition of the foam.
Some skis have a dampening system built in.
The idea is to absorb vibrations and avoid chattering. Usually it's some sort of elastic material or a piece of metal attached to the ski in a strategic place by some sort of elastic material. Of course it adds a bit of weight to the ski. Having light skis isn't everything. Ultra-light skis will be biffed around by piles of crud or difficult snow but jump turns are easier.