Nematodes are important parasites of people and animals, and in natural ecosystems they are a major ecological force. Strongyloides ratti is a common parasitic nematode of wild rats and we have investigated its population genetics using single worm, whole genome sequencing. We find that S. ratti populations consist of mixtures of asexual lineages, widely dispersed across the host population. Genes that underly the parasitic phase of its life cycle are hyperdiverse, compared with the rest of the genome. These patterns of parasitic nematode population genetics have not been found before and may also apply to Strongyloides spp. that infect people.