Try this for vinyl siding.
Three parts hot water, one part bleach, and a healthy shot of dishwashing soap. Wet the siding with a hose, Scrub the mix on with a long handled scrub brush, and let it set for few minutes. Rinse from the bottom up to keep all the dirt from streaking the wall.
For very little cost and effort, this technique does a amazing job. I had a vinyl sided place with a long wall, facing north, that would grow mold spores, and funky green patches in the shade. Once a year I would spend an hour with the scrub brush and the hose, and it would look new when it dried.
I haven't heard about damaging house wrap with a pressure washer, and it certainly make sense, but I have seen the damage you can do if you don't know what you are doing when using one. Everything from needlessly blasting paint off siding, and putting deep grooves in wood decking, to damaging sheetrock ceilings by blasting water past soffits and in to attic spaces.