I have met many strange people in my life, and I believe I'm a weirdo myself, too, but here are my top 3 shortly:
The bicycle lady. She's in her late 50s, very tanned, extremely fit - and bicycling near my parents' house every day. It seems she was bicycling between two town centers (about 15km in between) all day long, no matter if it was sunny, raining, snowing.. What makes her weird is that she was spitting on people. If anyone else was walking or bicycling on her route, she always spitted on them.
The wrist watch guy. As a young adult, I worked at an open air market selling flowers and berries. One day, a guy came to chat with me. I was about 18-19, and he was 30+. One head shorter than me, and wearing a shabby track suit. We had a polite small talk, and he asked to take a closer look of my wrist watch (basic Fossil watch with dark brown strap). I was confused, but let him look at it, and he was examining it for a good 5 minutes with a creepy, ecstatic face. Then he gave it back, and drove away in his tiny Fiat. The guy kept coming to our stall almost every day, wanted to take a look of my watch while telling me watch related facts... My colleague told me later that he was also obsessed with her (=teenage girls') basketball team. Went to see all of their games and memorized all the public information of the team members.
My cousin who lived with my parents. He has done (and keeps doing) the weirdest, stupidest stuff, but this is the best example of him being really strange. He was approaching 20 but still had plushies and watched TV shows meant for toddlers (like Teletubbies). He had a Krtek (the Czech mole) plushie, and after shower or sauna, he used to sit on the living room sofa half-naked. Krtek in one hand and his dick in another, making a dialogue of Krtek and the dick chatting together.