So how could I make a checker texture distorted like most other blender textures in the material nodes category?
Well the only inputs that can affect distortion on the Checker texture is the Vector input and the Scale input. You can plug the colour output of any other texture node into either of these 2 inputs to distort the checkered effect quite dramatically.
Solution 2 - Distortion created by mixing Texture Coord and Noise texture with more subtle effect.
Please note the Subtract node is optional and is used if the texture doesn't reach the edge of the object. It is used to offset the texture so that it fills all surfaces of the object.
Credit for this technique goes to Bartek Skorupa in his Manipulate texture coordinates like a boss presentation.