Can a pilot or airliner be responsible for injuries caused by turbulence?

Maybe so. Pilots are not able to change the weather or eliminate all turbulence along your flight path, but some turbulence can be expected depending on the prevailing weather conditions. If a pilot negligently or carelessly wanders too close to a thunderstorm (for example) and turbulent air from that thunderstorm shakes the plane and causes you injury, you may have a viable plane injury accident claim. Conversely, if the pilot’s radar shows clear skies and he or she accidentally hits a patch of turbulence, you may not be able to hold the pilot responsible for injuries you sustain.