It's tough to pick the one weirdness which rises above the rest.
Let us suppose a Cartesian plane of eccentricity. The positive Y axis corresponds to hyper-intellectual oddness: something bizarre done due to one's beliefs. The negative Y axis corresponds to hypo-intellectual oddness: something bizarre done out of sheer animalistic pleasure. The positive X axis corresponds to social oddness: something weird only in relation to social context. The negative X axis corresponds to asocial oddness: something odd done alone.
Some examples would help.
Quadrant I contains weird things one does out of beliefs, in public (or involving other people). This can include such things as spitting whenever saying the name of John Foster Dulles, carrying an umbrella to prove the universe really is out to get you, or speaking Lojban to store clerks.
Quadrant II contains weird things done alone out of conviction. This can include such things as teaching one's cat to recognize zombies, learning everything possible about Welsh history, or practicing Christopher Walken impersonation Just In Case.
Quadrant III contains weird things done alone, out of the sensory pleasure they provide. This can include such things as always wearing socks in the shower, juggling stuff while walking around, or using a bearskin rug draped over a hammock as a bed.
Quadrant IV contains weird things done, in public, for the sheer pleasure of doing them. This can include such things as speaking in Cockney rhyming slang or Clockwork Orange argot, walking about with a ferret curled around one's neck, or always wearing a skintight catsuit (note that if the catsuit is in case one encounters the opportunity to catburgle, this falls into Quadrant I).
Having made these distinctions, I can list my top eccentricity in each quadrant.
I. I once tried communicating only via mumbles, just to see how much communication is possible. Quite a bit; mumbles carry just as much information as enunciated smalltalk.
II. I have a machete under my bed for when zombies arrive.
III. I often babble tala bols to my cats. ("terikitatadadinDHA")
IV. I once wore pijama pants to a wedding reception.