Which side?

Left

left here and left handed?

Center

Right handed but always hang left. I have tried right and it feels odd

Almost every guy has balls that hang at different levels. Those that don't are the ones laying on the floor and have green looking faces.

I have made the same observation about which side one hangs too, in pants. I go left and my left ball is lower than my right. I have noticed the same with two friends, the one that was the same as me also wears left, the other wears right and his right ball is lower.

I am left-handed. My penis points to the right.

It wasn't so long ago that if you were having trousers tailor-made, the taylor would ask which side you "dressed" on. The crotch could made to be off-center so the package could hang comfortably. Your package always showed. Trouser crotches were fitted as high as the base of the penis.
this was before brief became popular. The girls ,in those days, knew what they were going to get and how "long" it was going to be!!