Whenever there is conflict and oppression in the world, there are people who leave to find a place that offers greater liberties and freedoms. People, generally speaking, prefer to live among a similar culture and religion, and refugees would prefer to be able to return to their homes, so the solution to the refugee crisis is to give incentives for the governments of the world to let go of their power games that are so oppressive to the people.
The legislative branch of the proposed international government will have two Houses. The House of Representatives will address legislation that is based on the Will of the People, and the Senate will address legislation based on the Rights of the People. Our Founding Fathers understood they had to find a balance between states that are large and small and densely populated and sparsely populated, and so they chose a bicameral government based on rights and will of the people. States with greater population have more say in the House of Representatives and smaller states have more say in the Senate.
One right citizens of the international government will have is to be able to leave their nation if they believe they are being oppressed. If a government is oppressive to the people, their people will leave and that nation will lose power on the international level.