This page (https://alleninstitute.github.io/AllenSDK/unionizes.html) gives a quick summary of what each property represents, so you could pick the one that best applies to your work. There are a few things to consider when using these various metrics as measures for connectivity strength.
Projection density measures the ratio of projection pixels to the total number of pixels in a structure. As a result, your choice of structure (ontology level) impacts the resulting density measurement. If your question of connectivity strength involves how much of a structure is projected to, then this can represent that.
This metric measures the intensity of the signal by comparing the sum of projection pixel intensities to the sum of projection pixels. The value of each pixel containing projection signal is its intensity at that pixel. By comparing the sum of the values to the sum of the pixels, an average intensity across those pixels can be found. For example, a structure can contain some amount of projection signal across most of its pixels, meaning the projection density would be very high. However, most of this signal could be rather weak (in intensity) so that the projection intensity within this structure would be low. Or, a structure can have a few pixels with projection signal, so that the projection density is low, but the signal in those pixels could be very intense, so that the projection intensity would be high.
This is a product of density and intensity, which directly relates signal strength (pixel intensity) to the size of a given structure (total number of pixels in the structure). A widely spread, weak signal and a narrow strong signal may both have similar projection energies.
The projection volume is simply the total volume of the projection signal. Since larger injections in the same site would lead to more projections, the projection volume can be normalized by the injection volume to yield the normalized projection volume.
Dividing the projection density in a structure by the injection volume should be the same thing as using the normalized projection volume in a structure to calculate the projection density.