Why are most weapons in AC-130 on the left-hand side?
It is not designed to strafe, it is designed to loiter over a target or, to apply suppression fire or support fire for a sustained period of time.  

It often circles a target area and a counter clockwise orbit (circling to the left) makes sense since the captain sits on the left and can keep the area in view at all times.

Therefore, the weapons are mounted on the left.