The difference between Abnormal and Eccentric

When used as nouns, abnormal means a person or object that is not normal, whereas eccentric means one who does not behave like others.

When used as adjectives, abnormal means not conforming to rule or system, whereas eccentric means not at or in the centre.

check bellow for the other definitions of Abnormal and Eccentric

Abnormal as an adjective:

Not conforming to rule or system; deviating from the usual or normal type.
Abnormal as an adjective:

Of or pertaining to that which is irregular, in particular, behaviour that deviates from norms of social propriety or accepted standards of mental health.

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.