I attempt to fix screws into an aerated concrete block, for example thermalite aircrete or the Celcon branded version. I use various plug options such as Molly nylon rawl plugs, nylon aircrete spiral plugs, plain heavy duty wall plugs, Plasplugs and even just basic screws alone. I discover that simply screwing a screw into the aerated block using a basic screwdriver is as good, and even better than using plugs. I also decide that the nylon spriral plug works really well, except I don't have the correct drill bit to start with, so I crack the brick on my second attempt. I wasn't successful at all with Plasplugs, the Molly plugs were to big for me to find a suitable drill bit. I don't know the name of the screw that I had success with, but they are extremely strong.

See my video (Part 2) where I use vinylester resin and threaded rods, instead of screws, and it works much better.
https://youtu.be/vouvdOwLBvg