Depending what one means by "oddball" there are some fish that may fit your interpretation.
Thinking single species fish for the tank, African Butterfly fish are interesting, though many find them boring because they just sit at the surface motionless until prey appears then they jump into action. Any fish approaching the surface will be eaten or bitten into, and these fish have enormous mouths. I had a pair for many years in one of my several tanks then, but if this was the only tank I had had, I doubt I would have found them very interesting. Except when feeding, or interacting, they are much like "pet rocks," lol.
Thinking more of community-acceptable fish, I am very fond of the whiptail catfishes. There are two types, the smaller common Whiptails in the genus Rineloricaria such as R. parva, and the much larger "Royal" species in Sturisoma. The Rineloricaria [some sources may have these classified in the genus Hemiloricaria] remain at or under five inches (11-12 cm) and as they are not active swimmers they suit smaller tanks like 3-foot quite nicely. You could have one, two or three. There is also the Red Lizard Whiptail, scientifically classified as Rineloricaria sp. L010a, which is just a tad smaller at 4.5 inches max, and an interesting brick red colouration though over time this seems to become less intense and more brownish-orange. All are peaceful and get along nicely.
Of a similar "prehistoric" appearance are the Twig catfish. The smaller species in Farlowella are again better than the "Royal" species which get much larger and can make quite a mess. These are true vegetarians; the genus was named by Carl and Rosa Eigenmann (1889) in honour of the American botanist from Harvard, William Gibson Farlow (1844-1919), who specialized in algae plants. And this is certainly one of the finest algae-eating fish, excellent at eating common green algae and diatoms, much the same as otos and Bristlenose plecos, but will not touch "problem" algae like black brush/beard, hair, etc.. But one caution, this fish with its continual grazing of all surfaces including plant leaves can damage fine-leaf plants. It is fine with hardier plants like the large swords, but my chain swords developed holes in the leaves and there was no doubt it was due to the Farlowella vitatta.