If you have a Schengen passport you can stay in the country for 6 months at a time to apply for work. The ones who are allowed to enter the country by family-reunion, will have legal rights accordingly, but their permit to stay and work will be dependent upon the family member they are united with (usually the spouse) for several years. If you have a legal stay in another Schengen country, but have a passport from another country, you can stay in Norway as a tourist for 3 months, but cannot obtain a work permit.  As a tourist you have to prove that you are able to support for yourself and your return.  If not you will be sent out of the country.  Many are denied entry for this reason.

In principle, there are no legal differences between native and migrant sex workers involved in prostitution. There are no regulations that can be used to deport or deny residence because of sex work (as it’s neither work nor criminal). 

Migrant striptease and dancers will not be given artist’s work permits.  It is a very limited marked in Norway and of less practical importance at the moment.

In practice:

The police enforce the Alien laws quite heavily with migrant sex workers. There are regular controls resulting in deportation if migrants who cannot show valid identification papers, permit to stay or money for their own support. 

If migrants claim to be victims of trafficking they are offered a 6 months stay including a permit to work, a so called reflection-period. 

Obtaining asylum as a refugee is very hard and decisions are made fast, so there are few sex workers who apply. Norway also enforces the Dublin convention strict.

As written before, work and residence permit will not be given for work in the sex industry, neither prostitution nor striptease.