As a citizen of the EU you have certain rights. You can find the details at:
http://fra.europa.eu/de/charterpedia/title/v-citizens-rights
If you have arrived in Germany as a refugee, your status depends on different factors:
There are four different statuses for refugees. Two statuses are for accepted refugees, the other two for not accepted refugees, but these do also grant a certain limited right to stay in Germany.
You can be accepted as a refugee according to the German basic law (“Grundgesetz”) as stated in the article 16a or according to the Geneva Convention. The criteria of the basic law are quite strict, because the reasons to leave the home country have to be based on political persecution. That means that a person is persecuted by its own state. The criteria of the basic law do not cover people who want to escape war or hunger. For this group of people, the Convention of Geneva applies.
Depending on your status as a refugee, you might be told to live at a certain place in Germany and cannot chose to move as long as your status does not change to one where that would be allowed.
If you are accepted as a refugee because your reasons to leave your country in fear of persecution is proven as stated in the German basic law or the Geneva Convention, you are allowed to work in Germany and chose your place of living.
If you cannot be accepted as a refugee, you might have a status as a “subsidiär Schutzberechtigter” (a person eligible for subsidiary protection) if you are in danger of torture or death in your home country. This status will be set for one year and then re-examined. During this period, you might be forced to live in a fixed place because of the support via social welfare, but you are allowed to work.
If you do not get one of the above-mentioned statuses, you are moved to your home country / expelled from Germany. It is possible to suspend your duty to leave Germany for a certain amount of time. This situation is called “Geduldeter”. This status will be re-examined every six months. The following reasons result in a suspension: international legal reasons, humanitarian reasons, reasons concerning the political interest of Germany.
If you are in the status of “Duldung” you do not have an allowance to stay. After six years, the status may be modified, so you might get the right to stay in Germany.
The status as an asylum seeker is only true as long as your application for asylum is not decided on yet.
For further details see:
https://www.anwalt.org/asylrecht-migrationsrecht/fluechtlingsstatus/