Snapping to Grid
 

For some reason, all the objects on my grid keep snapping to grid, although the icon is off. And no, I'm not holding "J" :p. Can anyone tell me what the problem is here?

Well to begin with, holding the "J" key wouldn't do anything unless you changed the default settings. To snap to a grid you hold down the "X" key.

However, I would check your move tool settings to see if you have discrete move turned on. That could act like snapping to a grid.