Select a brush in the brush panel. Drag to the art board and add additional paths such as spots and dots / circle paths to the artwork. Drag the stroke and additional paths to the panel
Another way to quickly add a lot of spots etc is to use the symbol sprayer and add those sprays to the path and then re-define that as a new scatter / art etc via the panel. You can also use the symbol sizer tool and symbol scruncher tool to create smaller and more dense spots (made up of dots and stars and lines and any other designs you have added to the mix) to the stroke
Use the live effect 'glass' and the appearance panel. Select a stroke. Go to the distort menu and glass and apply a distortion (at this point you can also use a map from Photoshop). The odd thing with the filter gallery plugin is that is does not allow for multiple filters to be added in a single dialog: a quick way around this, and a quick way to added many levels of distress effect to the stroke, is to use the duplicate effect command in the appearance panel and add more and more glass distortions to the art. The more you add, the more likely the re-draw of the stroke will be slower though.
Use the Texturizer filter found in the texture menu. Select a stroke and go to the appearance panel and go to the stroke. Apply the Texturizer filter (as well as others). Changing the settings for this effect and add a texture via the drop down and browse for a PSD file or use one of the default ones. Set scaling as required. To remove the effect, simply go to the appearance panel and use the right side menu and clear appearance
Take a photo of a texture such as a wall etc and transfer to your computer and open the image via the file / place command. Click the embed button and then go to the image and trace command and then to the trace panel and set mode to black and white and expand. Drag to the swatches panel. Drag the stroke from the panel. and select the path. Object menu and ungroup and remove the bounding box. Select remaining path and go to the appearance panel and right side menu and add fill and then select the just added swatch and then set the blending mode for the swatch to something like darken or multiply. Drag the stroke back into the panel and it will be created as a new scatter / art etc but it will now have the underlying image.