The weirdest things I've encountered have been in Pokemon Yellow and one of the original Ruby/Sapphire/Emerald games
In Yellow, besides Missing No. of course, I once found a level 121 Golbat. I flipped out and brought my mom in to see, but I was playing it on Stadium, because I wanted to play it on the TV, and forgot to save before I pulled the game out losing it forever. I was super mad about it.
Then in RSE, I was running low on my batteries and was trying to see how far I could get before they died. I got to the part with the Kecleons and a purple Kecleon showed up. I flipped out thinking "OH MY GOD IT'S A SHINY! MY FIRST ONE EVER" (I didn't know red Gyarados was shiny from gen 2, I thought it was just a thing in that game only) I threw my pokeball, caught it, and during the part after the battle where the screen goes black my battery died, losing that Kecleon forever. I spent over a week trying to get it to reappear. I looked it up years later to see how many others found one... and was honestly surprised when I couldn't get anything to pull up.
Both of those situations will no doubt sound fake, and if I wasn't there I wouldn't believe me either, but I'm still waiting for the day I'm validated, at least with the Kecleon, because my mom saw the Golbat, so I don't feel too bad about that one.
So anyway, what's your weirdest Pokemon stories, or anything like what I've encountered?