I don't know about Strangest, but one of the scariest. I was turkey hunting in the Lincoln Nat forest of New Mexico. I had walked in and was sitting under a big Oak tree. I had been working a slate call for a quite a while. I was getting answers from a few Toms, but had not seen anything. The sun had come up and was warming up the hillside I was sitting on. I started getting drowsy. I tried to keep awake and kept working the slate.
Suddenly there is a loud screaming, right behind me. Scared me to the point that I was in total panic. I jumped up, spun around and there stood a Mountain Lion. This lion had slipped up behind me, and was sitting there staring at me. I was so paniced when I jumped up I had dropped my shotgun. There I stood, no gun in my hand, looking at a Mountain Lion, just sitting there staring at me. I was afraid to bend over to grab the shotgun. In so doing I would expose my head to the lion and it would be on me before I could get the shotgun up into position. It seemed like an eternity before the Cat yawned, stretched, then turned around and left.
Grabbing my shotgun, I left in the other direction.