There isn't much of anything.
Firstly, if you go a long way out you eventually reach other stars, and these are distributed all round the sun, most aren't on the ecliptic, and those that are close to the ecliptic are only there by coincidence. Even further out are billions of galaxies across the universe. They are also not only found in the plane of the ecliptic.
Coming in, the sun's gravitational influence starts to be felt strongly enough for objects to orbit at about 1 light year. Here you can find some icy bodies in a sphere all round the sun (The Oort cloud). They are very widely spread out over huge volume of space. Most are not on the ecliptic.
As you get closer in, you find objects that probably formed in the plane of the ecliptic, but after an interaction with a planet, they were kicked out of the plane. They now orbit the sun in the "scattered disk" they aren't distributed randomly, but they may be more than thirty degrees from the plane of the ecliptic.
There are also comets. These are objects from the Oort cloud that have (for some reason) fallen towards the sun. As they fall from the Oort cloud, they can be very far from the ecliptic.
Asteroids are mostly close to the ecliptic, but a few are very far from the ecliptic, with about 250 on orbits that are inclined by almost 90 degrees. (source)
Inside of the asteroid belt there is very little apart from the four terrestrial planets. The sun's influence here will tend to cause dust either to be repelled or to spiral towards the sun. Space here, and to the edge of the solar system is filled with the solar wind, which formed of charged particles of the sun's atmosphere, flowing out through space.