I see enough ambiguity in the definitions to warrant the question.
To dodge someone|something is to avoid them|it because you don't want them|it to see you or accost you.
We might dodge an organized crime "hit man", or dodge a question.
To shun someone|something is to avoid them|it because you have chosen to ignore or "turn your back on" them|it.
The difference lies in the motive and also in the manner. Dodging is done on an ad hoc basis, when the need arises. Shunning is planned and deliberate and ongoing.
We might shun an acquaintance who committed a felony, or shun casinos.
In Pennsylvania where I live (and elsewhere) the Amish, a religious community (who are portrayed in the film Witness by Australian director Peter Weir) will shun a member of their community who has committed in their estimation a very serious sin; they treat the person as though he or she did not exist.