I think you are
I need no definition
Everyone is familiar with words, that is, they need no introduction.
Also, language users can understand words even if they are unable to formulate an explicit dictionary definition.
Flowing like water,
From port to port.
This seems like a poet description of words coming out of people's mouths and into people's ears (from port to port).
This is an allusion to the old adage "Sticks and stones may break my bones, but names will never hurt me."
I am mightier than the sword.
This is an allusion to the adage "The pen is mightier than the sword." (This clue was a big giveaway.)
Many tremble beneath my power.
But I may be purged from afar.
I'm not sure about these lines. Maybe something about fear, stuttering, censorship, and/or electronic communication.
Both good and evil.
Martin Luther King Jr. used words; so did Joseph Stalin.
I am undetermined until the thinking makes me so.
It is in virtue of human thought that words have meaning. (At least some philosophers of language think so. For example, Paul Grice.)
Thought is also useful for disambiguating words, for instance, deciding if an occurrence of "bank" refers to a river or a financial institution.
Spun in to anything,
"Spinning a yarn" is an idiom meaning to tell a story.
Given the generativity of language, and the fact that language contains open classes of words, stories can be about anything.
I can motivate the masses.
Words can be used to persuade people. Rhetoric (on at least one meaning) is the study of this use of words.