Why there is no axis measurement when telling distance between objects in space ? What's in upper part in our galaxy ?
If space is 3 dimensional, what lies beneath solar system, or in upper part ? Why it seems from every graphical view of solar system / galaxy, everything is in one single axis ?
You might benefit from watching this Minute Physics video on Why the Solar System is Flat. A summary is due to the way objects in our solar system and particular galaxy are drawn around a central massive item by gravity. Through the conservation of this angular momentum, and the loss of vertical motion though collisions, the solar system and galaxy "look" flat. 

Talking of "upper" and "lower" doesn't really make sense in space. Gravity feels like it's pulling us down on Earth, and that is why we have this concept, but in space we lack this reference. For our own purposes, humans have created an artificial means of determining points of reference for spacial coordinate systems. Due to the rotation of the Galaxy we have established a base plane called the Galactic plane, from which a coordinate system and sense of "up" and "down" might be inferred (I think our solar system tilts at a 63 deg to the galactic plane of the Milky Way). In the context of Earth and our solar system, we use the plane that the Earth "makes" as it circles the Sun as the point of context for the Earth's axial tilt; we call it the ecliptic plane. 

As for the rest of the Universe you may wish to check out this blog post from Cornell called Why is the Universe flat and not spherical?. Basically the Universe has a slight curvature to it but since we are on the surface, and have a limited view, it is difficult for us to see anything but flatness. This is related to why graphical views appear flat. Graphical views are generally limited due to our point of view and the sheer astronomical size of distances in space. Even in "dense" super clusters there are vast distances between objects. Overall it's easier to linearly show things rather than as they truly might be.