As in most such scenarios, a cross sectional or case control study will be the most rapid, cheapest and most feasible study methodology. If there are many separate health concerns expressed or possible as in this case an initial cross sectional survey will allow for an assessment of exposures, self-reported health outcomes and concerns. If there is one clear cut health outcome of interest one might go forth with case finding and a case control study.
Alternatively one could perform a health survey with medical screenings of a given population(s).
Click on the link to Survey in the sidebar on the left.