Here are examples of the word/phrase "eccentrically" used in a sentence and paraphrased in a sentence...
He was eccentrically excited to be at work today.
He was unusually excited to be at work today.
Those foreigners eccentrically communicated with each other using sign language.
Those foreigners unorthodoxly communicated with each other using sign language.
Wow! That man is eccentrically wearing socks with slippers.
Wow! That man is unorthodoxly wearing socks with slippers.
Other Examples...