I am not really sure how to make it stronger because every time I change settings, nothing really changes (in blender render).
The viewport AO uses different engine than the bake AO function (Blender Internal or Cycles in 2.79 Blender), so the settings for the viewport AO are not used in the Bake.
The viewport AO is multiplied by 5, so if you take your baked AO into Photoshop or another editor and you play with the levels of the image (or you multiply 5 these images on top of each other) you get similar result.
Selected to Active does not have impact on the strength of AO, only from which object it will get calculated.
In your bake options you have 'Selected to Active' enabled. For ambient occlusion, you should just be able to bake the ambient occlusion of your object without baking it from another object. Unchecking this option should result in a more intense bake, as well as make the settings work as expected.