Seems preety damn useles to me.

see picture


with sway when you dash left/right then you move forward and to the side - it's probably for dodging and attacking, so you dodge and move forward, with dash you can either dodge or move forward
when you don't use dash then it's really useless
and with sway you move less forward

It's for dodging and while still allowing you to close in for those melee moves.
Like the picture above, instead of going straight up to the right or left, you go forward at the same time.
So you can spam left right arrows instead of just pushing your up arrow.
Works great with things like Mighty Byne, Squealer, and Exroad.
Jikuns don't need it cause they just spam jump and wolf tackle already.
Basically useless for small lands that work far better with short boost instead of it.
They don't run together.

You two know you can already dash diagonally without Sway, right?

The differences between Sway and a regular dash are:

-Sway doesn't move as far as a dash
-You move faster during Sway; this makes it better for sidestepping oncoming attacks
-Sway is spammable; you can chain sways much faster than you can dashes
-Sway can't move perfectly sideways, you'll always move slightly forward diagonally. Backwards diagonals still work too though, if you don't want to advance. Forward diagonal sways move at a sharper angle than simply left or right sways.
-Sway is invincible on startup. If you've ever played fighting games, think of it as being usable to DP through an attack with good timing.

Mainly you throw this on small S-lands that you want to be difficult to hit. CBJP has a few Zero Saber Girls that use it. You need to know what you're doing to make it effective, though.