The biggest part of the sway is controlled by the friction of the bars on the L-bracket. So you never, never, never want to put any kind of grease or oil on those L-brackets. Yes, they will groan and pop some, but that means they are working.
The pivit points are just that, joints for pivoting. Those can be oiled, but I've never oiled mine, ever. I just spray my hitch ball with some WD-40 every time I hitch up. This way, I don't have a greasy mess when removing the hitch from the truck receiver. That is the only thing I put oil or grease on ... the hitch ball and the coupler on the trailer. Keep everything else on your Equal-i-zer dry.
