Field mice always sleep facing northwest. Kangaroos can't walk backwards. Female hyenas have penises. Let's face it, nature is weird. What's the strangest thing you know about the animal kingdom?
Wait, this is a little misleading. The female spotted hyena doesn't have an actual penis. It's just a very large clitoris that also functions like a urethra/vagina. I mean, the penis and the clitoris stem from the same place during fetal development (ah, the things I learned in Psych 101: Sex and Gender), but in female spotted hyenas, it's technically a clitoris.
...Anyway. To answer the question, nature is weird. I don't know what I'd consider the strangest animal quirk, but for one thing, I think the platypus is one heck of a weird animal. It lays eggs, even though it's a mammal. The males can poison you with their feet. They have duck-like mouths. And more! Of course, the platypus is the most obvious choice. Then there are those lizards that squirt blood from their eyes. And turtles! Oh, and those humans are pretty weird, too. They're practically bald all over the place except for a few areas, even the ones who are fuzzier than others. They're pretty ugly compared to the general animal kingdom. They can't even smell very well, unlike most other animals. Not to mention the devastatingly parasitic effect they've had on the planet.