I want to create something like this:


Here is it without the wireframe:


I managed to get the shape right (with sharp edges, not rounded off like in the picture) but when it comes to smoothing, I always get an unrecognizable blob. Can anyone help me please?

Probably you need more subdividing polygons for the meshsmooth to work the way you need. Add them to the areas you want smooth more (the edges of the objects).
Hopefully that makes sense?

To experiment with the concept I'm talking about, create a simple box mesh with 12 edges and add a meshsmooth modifier. It will deform into a blob. Next select the edges and chamfer them, or select a polygon and slice it, to see how the meshsmooth affects the box's topology.