I have a pair of African Clawed Frogs... George & Weezie. I got them when they were very small and now they're almost the size of leopard frogs (especially Weezie...she's FAT! LOL). I've had them about 10-12 years now, and they're still going strong!
If rats are considered odd pets... I have two: Lucy & Hazel. They are very inquisitive and demand to come out and play every time they see me.
I had a curly haired Tarantula named Alice until about 3 years ago. She was around 15 when she finally died. I also had a box turtle for almost 20 years (he was a free range house turtle ... 4 years ago someone left the door open and he ran away! I'm still not over that.)
About 7 years ago, I had a pet crow named Jibber. I found him as a nestling, he had been mauled by a cat or some other animal. Because of that he couldn't fly and had some issues with his legs, but still managed to get around very well and do mischief. He was like a 2 year old with feathers! I miss the little guy.
I've also had a rehabbed American Robin, plus pythons, boas, rat snakes, and various other snakes, a legless lizard, green iguanas, hermit crabs, and anoles.
And those are just the "odd" pets...
~Lily