"Hello again! How are you doing!?"
I was pretty bewildered by this young, attractive woman stopping me in the street and asking me all sorts of questions as if she knew me. I was too bewildered to speak, even, and she started going on about her new job, how she wasn't getting along with people, and how her home life was causing her stress.
I managed to speak at this point. I believe I said; "Er..."
I am a master of the cutting remark, as you can see.
Anyways, horror dawned on her face (her quite attractive face, I may add) and she said.
"Oh, yes. Right. You don't know me do you?"
And with that she walked out of my life.
May not have been the strangest single thing anyone has said to me, but it was a bit of an odd encounter.
There was another time I was in a Games Workshop store (For those few of you not in the know here, Games Workshop sell several tabletop wargames, and models and paints for said games. Not much else.) and some guy walks in. He calmly allows a staff member to show him around the shop floor, examines some of the games on display, bemusedly watches two guys play a few turns of a Warhammer game and then he asks for a computer game title.
He is informed that Games Workshop do not really sell computer games.
Then, the guy turns around and (deadly serious, absolutely no sarcasm, I promise you) says:
"Oh, it's just the washing machines and stuff like that you sell here? Ok."
With that, he walks out of the store, leaving some very confused people in his wake.
I also once had a guy ask me to wrestle him. Quite randomly. He then proceeded to attempt (without success) to tear a drainpipe off a nearby wall. Then he punched the drainpipe and started yelping and sucking his hand.
This last one wasn't really strange. It was damn funny, though!