The difference between Eccentric and Outré

When used as adjectives, eccentric means not at or in the centre, whereas outré means beyond what is customary or proper.

Eccentric is also noun with the meaning: one who does not behave like others.

check bellow for the other definitions of Eccentric and Outré

Eccentric as an adjective:

Not at or in the centre; away from the centre.
Eccentric as an adjective:

Not perfectly circular; elliptical.

Examples:

"As of 2008, Margaret had the most eccentric orbit of any moon in the solar system, though Nereid's mean eccentricity is greater."
Eccentric as an adjective:

Having a different center; not concentric.
Eccentric as an adjective (of a person):

Deviating from the norm; behaving unexpectedly or differently.
Eccentric as an adjective (physiology, of a motion):

Against or in the opposite direction of contraction of a muscle (e.g., such as results from flexion of the lower arm (bending of the elbow joint) by an external force while contracting the triceps and other elbow extensor muscles to control that movement; opening of the jaw while flexing the masseter).
Eccentric as an adjective:

Having different goals or motives.

Eccentric as a noun:

One who does not behave like others.
Eccentric as a noun (slang):

A kook; a person of bizarre habits or beliefs.
Eccentric as a noun (geometry):

A circle not having the same centre as another.
Eccentric as a noun (engineering):

A disk or wheel with its axis off centre, giving a reciprocating motion.

Outré as an adjective:

Beyond what is customary or proper; extravagant.
Outré as an adjective:

Very unconventional.