Each state is different as to the requirements and duties.
We have volunteered in many parks in the country, both state and national, and most of the gigs we got was by visiting the park in person to see what the 'atmosphere' of the park was, talking to the current hosts about the duties and if they were happy there, and then we inquired at the office if the park suited us. They really were impressed that we were there in person so they could interview us and get a 'feel' about us. It worked for both us and them.
We have never taken a position where bathroom cleaning was required. Many parks have their own maintenance departments for doing that. We have worked in the entry station booth signing in campers and general 'in the campground' presence with walking the campground a few times a day and visiting and answering questions. Our best positions have been interpretative - giving lighthouse tours is our specialty.
Volunteering is a great experience knowing we could help out. We enjoy meeting new folks and helping them, if needed.