Is there a Photoshop or Illustrator action or a set of brushes that can help me achieve this image style and feeling in my drawings / photos?
Check out the Brush and Brush Presets windows. I recommend trying the Dual Brush settings to get a similar texture like your image. Using default brushes, pick one brush that's the base(something not too jittery) and another that's going to be your texture(grungy). Try adjusting the brush sizes and spacing to fit your need. I made a path, and used 'stroke path with brush' and filled in the center with white. Mine is a bit messy, but you get the idea I hope.
There are also a lot of custom brushes people have made, but I think searching for one might take longer than playing around with Dual Brush. Plus, you learn this way :) Hope that helps.