eccentric has 17 distinct synonyms spread across 4 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is concentric.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
conspicuously or grossly unconventional or unusual
“restaurants of bizarre design--one like a hat, another like a rabbit”
not having a common center; not concentric
“eccentric circles”
Synonyms, antonyms and the broader and narrower relations for eccentric come from Princeton University’s WordNet. Full sources and licences.