How can I straighten the shape line in the picture without losing the objects solid form? I usually use ctrl s and 0 to do it, but, that doesn't work in this case.
I think that the most simple and versatile method is to use a LoopTools addon and it's Relax feature. This way you can also straighten / relax / smooth multiple vertices which should be almost impossible with the 3D cursor solution above. For me this addon is a must-have for modeling anyway so I am sure you won't regret installing it.
You can double click G and slide the vertex all the way to one of the connecting vertices. then slide back where you need the vertex to be and you will have a straight line.