If I had to vote for the single weirdest place in the Solar System, my choice would be Jupiter's moon Io.
Io is the innermost and third-largest of the "Galilean moons" of Jupiter, the ones that caused so much trouble for poor Galileo Galilei when he observed them in 1610 and informed the Catholic Church powers-that-be that we aren't the center of the universe. It wasn't until the Voyager flybys in the late 1970s that we could see it as anything more than a fuzzy dot, even in the largest telescopes; the first close-up photographs invited comparisons to a moldy pizza, Detailed photos from the Galileo probe in 1999 confirmed the original assessment: Io is one bizarre place.
The first weird thing about it is that it is the most tectonically active place in the Solar System. Those pock-marks on the surface aren't impact craters, they're volcanoes. In general, the smaller a body is, the less tectonically-active you might expect it to be. Tectonic activity is (usually) triggered by convective fluid motion in a molten mantle or core, which requires a very hot interior to keep it going. The heat comes from two sources; the energy released by its coalescence during its formation, and the decay of radioactive elements in its interior. If that heat radiates away faster than it's being released, eventually the body cools off and freezes, and (most) tectonic activity stops. Heat dissipates more rapidly from a small object, so they tend to shut down much sooner. (That's what happened to the Moon, for example.)
But despite Io's small size, something is keeping it hot enough to create hundreds of active volcanoes. But what?
It turns out it's the proximity to Jupiter. The giant planet's gravitational pull creates significant tidal forces, and the stretching and compressing Io experiences generates enough friction in the moon's interior to keep the insides molten. The result: violent volcanic activity that spews liquid sulfur jets into the sky, creating plumes as much as five hundred kilometers in height. (It's the sulfur that's responsible for Io's bright colors.)
In fact, Io actually ejects so much material from its volcanoes that it has created a plasma torus around Jupiter in its wake -- a donut-shaped ring of charged particles tracing out its orbit.
Another cool thing about Io is that it's in orbital resonance with two of the other Galilean moons, Europa and Ganymede. Io is the innermost, and has an orbital period exactly twice as fast as Europa and four times as fast as Ganymede -- a stable configuration that has since been found in other systems with multiple moons. So every fourth revolution of Io, all three line up perfectly!
The reason this comes up is a new study out of Caltech that has found data suggesting an enormous underground magma ocean inside Io -- planetary scientists David Stevenson and Yoshinori Miyazaki believe the presence of a hundred-kilometer-thick liquid mantle explains the extremely active surface and its anomalous magnetic field, another feature Io shares with few other small bodies in the Solar System.
What lies deeper than the mantle is unknown. Some astrophysicists believe it has a metallic core, but that question is far from settled.
What's certain is that Io is a peculiar place -- sulfur volcanoes, seething lava lakes on the surface, continuous "moonquakes" caused by the tidal forces exerted by the enormous planet Jupiter looming overhead. And like anything odd and unexpected, it will continue to attract the attention of scientists, and we will continue to be astonished at what we learn about one of the weirdest places in our neighborhood.