In what ways can words be considered to have power

Influence.

Words have great influence over others. Examples of this can be seen in political campaigns, where candidates state their arguments, before actually having the power to do something about them. Yet, their words get millions of people to follow them.
This can also be seen in musicians and pop stars, who have wide-musical influence all over the world, such as Beyonce, Eminem, and other popular artists. 

With words only, one can start a new world order, or commit genocide (Actions of Adolf Hitler) and diminish a population.