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Collins English Dictionary
exodic
in British English
ADJECTIVE
1. of or relating to an exodus
2. physiology (of the motor or efferent nerves) transporting influences away from the spinal cord

I came across this word today in connection with early maps of the "Holy Land". They tended to include a representation of the route taken by the Israelites after escaping from Egypt, hence "exodic".
My copy of the OED includes the word with the same first meaning as above, but without quotations, just a note to say that it appears in "some modern dictionaries". Other dictionaries, including the Concise OED restrict themselves to the medical term.

Every other source I found on the internot gives the second meaning, and in the same words in the same order. Everyone copying everyone else?

However, a contemporary non-medical use might be thus: I'm glad I already live in the path of totality for the eclipse. The exodic routes from my city will likely be clogged that evening and the next morning.