Exhaust the internal route first
Almost every oversight body will ask whether you complained to the organisation itself and gave it a chance to respond. Keep dated copies of everything, including replies that say nothing.
Then the statutory body
In Ireland, the Irish Human Rights and Equality Commission handles discrimination and rights complaints and can take up systemic issues even when it cannot fix an individual case. Write to your TD in parallel: statutory bodies act faster on cases legislators are asking about.
International routes
United Nations special procedures accept individual submissions on urgent human rights concerns from anywhere in the world, and treaty bodies review states periodically. These are slow and public, and best used when domestic routes have genuinely closed.
Copy the organisations working on it
When you write through Let Us Say you can copy human rights bodies, charities and monitors working on your issue. They cannot always reply individually, but volume and pattern are what put an issue on their agenda.