The EU has the power to legislate and adopt binding acts in these fields. Includes free movement of persons (border controls, asylum, immigration), internal market provisions (goods, services, contracts, consumer protection, competition law etc), economic and monetary union, justice and security, anti-discrimination.
The EU and Member States may adopt binding acts in these fields. But Member States may only do so if the EU has not chosen to act.
Member States have the power to legislate in these fields. The EU may only support, co-ordinate or complement Member State action.
International law becomes part of the domestic jurisdiction once fully ratified by the state. Its provisions may be enforced via the domestic courts.
The state becomes bound by the terms of the international law once it has ratified it, but its provisions are not enforceable via the domestic courts unless domestic legislation is passed to effect this.