The Warp node will warp the input map, according to the intensity input map, and the intensity level defined in the parameters.
The Directional Warp will warp the input content in the direction defined in the parameter.
The intensity of the effect will be influenced by the intensity input and multiplied by the intensity parameter.
Vector warp is an advanced distortion effect, similar to Warp and Directional Warp, with the main difference being that it is driven by a (color) vector bitmap rather than a grayscale map. This means it is more powerful and versatile than its atomic node cousins.
The Vector Map is similar to a Normalmap, but it does not need to be normalised and only the R and Green (X and Y) channel are used. Blue and Alpha channels can be left black if you want. Constructing a good Vector Map can be the biggest challenge in using this node; you can either convert grayscale maps to Normal, or construct the map by combining channels with RGBA Merge. Alternatively, something like a "Flow Map" is also useable.
This node can be useful when you want to do very specific distortions with varying directions, where standard Warp nodes don't cut it.