I remember a few years back they had caught a Piranha in Pymatuning Lake ! Probably tossed in by someone who had a fish tank but it was caught by a local fisherman.
 
I caught a small Trout out of lake Erie years ago that had a plastic ring around it's entire middle body. The ring looked to have been on for some time it was distorting the fish's body shape. I swear when I cut it off that fish said ahhhhhh that feels better.

I've got a few fish stories.

-A few years ago I was fishing in a delayed harvest section of my local creek and caught an ~8" Largemouth Bass which is itself a rare species for this creek but even more weird was that it had a horizontal yellow stripe instead of a black one. Very odd and I've never see a bass like that since then.

-Not fishing but while scuba diving I'm Summerville Lake in WV, I encountered a ~16" melanistic smallmouth bass that was entirely jet black that followed me around the dive for about 10 minutes.

-While trolling in Erie last July, I was bringing up a cannonball with the lure still on the clip from 100' down in 133 FOW of off Northeast and I saw a fish twirling off of the spoon about 60 feet back. I unclipped the spoon and reeled the fish in thinking another big yellow perch with eyes too before its stomach, but soon realized we were too deep to catch them on anything, trolling or otherwise. I brought in the fish and sure enough it was a 20" 5# Chinook Salmon. No fight whatsoever so it must have been dragged around for a while and the dang clip didn't work right. Sure did taste good, though!

-A few years ago on 4th of July weekend we were drift fishing in PIB at night while watching the downtown fireworks. I hooked in to something big and eventually it came to the surface next to the boat and it looked around 26-30". To me it looked like a Walleye as it was the traditional greenish yellow color that bay 'eyes have but I swear I saw a barbel or two on it. My dad said it was a channel catfish but the mouth shape looked too predatory and the color was off. Sure enough, the fish broke the 6 pound test I was using at the time and swam away before we could boat it. Maybe it was a Burbot? But I highly doubt such a cold water fish would still be in the bay during the heat of summer in 77° water.

-Fishing in marina lake spring 2014 at the lagoons entrance. We were catching sunfish, small perch, and the occasional largemouth. Suddenly, I see a slow moving head poke out of the surface to the left side of the entrance with about a 12' wake from its large body behind it. At the right side were several adult and juvenile ducks. The head submerged and the wake disappears for about 5 minutes. Then, a huge splash and one of the ducks is dragged under, never coming back up. 3 minutes later, another duck goes under before all that were left finally fly away. Keep in mind, this splash had the size and noise of somebody throwing a bowling ball directly down at the water. To this day I have no idea what it was and the combination of that, stepping on the spine of a bullhead, and almost getting bitten by a water snake are why I limit myself to only swimming, snorkeling, and diving in the main lake now.

Blue fishing in New Haven Ct harbor a number of years back with a friend on his boat.
Waters in that spot  only a few feet deep and we were using surface poppers.
Suddenly he said  he saw a large head looking at us a few yards from the boat- I looked where he pointed, it was gone but a swirl was there.
Said it must have been a fish jumping but he was adamant that it was a big head and he saw eyes looking at us.
Hmmmmmmm--
 A few minutes later we both saw it a bit further out-- it  stayed up for a few minutes- seemed to look at us for a while.
Unsure what it was we moved away from that area to fish not wanting to snag it accidentally.
Weeks later the Ct Dep reported a Manatee had been in the harbor.
They had kept quiet about it not wanting folks to run all over looking and possibly cut it with props in the low waters where it hung around.
Manatees normally never get this far north but this one had reportedly  made the trip a few Summers.

This is probably the weirdest thing I've pulled out of Presque Isle Bay, which is saying something.
 
P.I. is a prehistoric playground, full of ancient fish, but if you think gar and bowfin are old, check this guy out-- Unchanged since the Cambrian period--500,000,000 years ago.  Actually, I should say "these guys." It's a colony of zooids called a Pectinatella magnifica, a freshwater bryozoan. Each rosette contains 10-18 zooids and each zooid has whorls of microscopic tentacles that they use to catch food in the water. Inside is a translucent jelly. This one was a little bigger than my hand, but they can get up to 2 feet!
 
Ended up on my hook while jigging underwater brush. Was hesitant to touch it, but they don't sting. Very lightweight and float through the water with ease.  
 

 
 

Maynard.G.Crabs
This is probably the weirdest thing I've pulled out of Presque Isle Bay, which is saying something. P.I. is a prehistoric playground, full of ancient fish, but if you think gar and bowfin are old, check this guy out-- Unchanged since the Cambrian period--500,000,000 years ago.  Actually, I should say "these guys." It's a colony of zooids called a Pectinatella magnifica, a freshwater bryozoan. Each rosette contains 10-18 zooids and each zooid has whorls of microscopic tentacles that they use to catch food in the water. Inside is a translucent jelly. This one was a little bigger than my hand, but they can get up to 2 feet! Ended up on my hook while jigging underwater brush. Was hesitant to touch it, but they don't sting. Very lightweight and float through the water with ease.     

Now that's one cool catch! I'd have been tempted to take it home for one of my tanks haha.

I've seen bryozoa at a few local lakes. Arthur and loyalhanna for sure. I have a few weird fish pics that im sure I've posted before, but photobucket is down for maintenance . Ill try and put them up later.

Same here FishinGuy, the stuff is pretty much common in all the area lakes, the history of Bryozoa (a/k/a. Moss animals) is amazing to say the least.
 
As for the Captain's inquiry; I'd have to say any pictures of me, holding any fish, is odd and rare. 

Although not quite exotic, a couple of years ago at Elk Creek I got a few of those Humpback (I don't know what the correct name is ) Salmonoids that showed up at Erie. It was different for sure. I threw it back, but was sure that no one would believe me until until more showed up. Now, this was before the internet & I never carried a camera. Was kinda pretty I thought.  sam

Mooneye? big tiger, 22" hybrid vigor! mutant hungry Lil guy saw these two goldfish (not koi) the next year in the same area jitterbug channel cat for size reference, I can palm a basketball.

Speaking of hungry guys !