Sodic soil?

I got some dry soil/clay from my yard and dropped it into some distilled water. The soil bundle collapsed almost immediately and when I came back 5 mins latter the soil was all on the bottom of the glass, whilst the water was very cloudy (but with the cloudiness being white rather than the colour of the soil). Does this mean that the soil is sodic? Is there any other test that I need to do to confirm this? Would gypsum help this soil?

It sounds like it is gypsum reactive. When you tested the soil did you touch it with bare hands? The salt on your skin can throw out the results. And the soil you need to test is about the size of a pea. If you did all this then gypsum will work very well with your soil but you need to also add it along compost.

Yeah, I picked it up with my hands. Also there was more than a pea size (perhaps as much volume as a broad bean).

After I came back about 4 hrs later the water was clear again (i.e. not cloudy). Is this an issue (i.e. is the cloudiness the salt or is it because the salt dissolves in water quickly and then releases all the other particles)?

The cloudiness can go but should still be there after 4 hours. If you can try again using rubber gloves, pliers, chop sticks etc to pick up a little aggregate of the clay you will get a better result. The aggreage is a bit of hard soil the size of pea, like a small version of the big clumps you get when digging up clay soil. Put it in the water carefully without dropping it and then watch. It should collapse then make the water cloudy. The cloudiness is the indicator you are looking for if gysum is worth the effort.