ZDoom

Warp2 effect has a 'direction' in which it creates the illusion of moving the texture. Is there any way to change it?

You need to build your own SHADERS, just play with values checking inside the main .pk3 file (not sure if you are using qzdoom, zdoom or gzdoom so) on \shaders\glsl\func_warp2.fp, create a folder called "shaders" and apply them on desired textures / graphics / sprites.