Object surface issues...

I know the title doesn’t explain alot. I’m terrible at explaining anything at all.
As you can see, I’m a newbie (to both this forum and Blender itself), and I’m still trying to get used to using Blender.
M’kay, anyways, I have a .obj composed of tons of stretched spheres and all that.
Meshes / objects overlapping each other. I’m guessing that might be the problem…?

So far, I used the “Smooth Vertex” thing since most of the answers I got mention using it.
It just butchered my model:

I wanna hide those little…uh, what would you call them…um, edges? Spaces? Whatever. Yeah, they look ugly, and I want to know how I can “blend” or “smooth” these out, like smoothing clay.