The Greek city was actually called polis (plural poleis). There were many Greek cities. One of the things that the Greeks did not do was to create a nation. They remained separate city states. In view of this, slave and women had vastly different rights. It all depended on which city you were a part of. For example, Spartan women were considered powerful and had certain freedoms. However, women from Athens had less power and it is even debated whether they could attend the theater. In terms of voting, both slaves and women were not allowed.
Status of slaves also varied considerably. Slaves were treated the worst in Sparta. Sparta was a slave culture. They subjugated a whole people (Helots) to do their farming, so that they could train in the army. Once a year Spartan young men would even go out to kill their slaves to keep them in a perpetual state of fear.
One final factor should be considered. Greek civilization lasted a long time. So, role over times changed.