Third country nationals, need to have a Swedish work permit in order to work and live in Sweden.
All information regarding working and living in Sweden can be found on the Swedish Migration Agency’s homepage: https://www.migrationsverket.se/English/Private-individuals/Working-in-Sweden/Employed/How-to-apply.html
The main rule is that you should apply for and have been granted a work permit before entering Sweden. The employer in Sweden initiates the work permit application by completing an offer of employment.
Persons who have lived in an EU country for at least five years with a residence permit may apply for long-term resident status in that country. Persons who are granted long-term resident status receive a special EC/EU residence permit. This type of permit in Greece is called επί μακρόν διαμένων – ΕΚ. This permit gives you certain rights, similar to those of an EU citizen and makes it easier for you to move to another EU country in order to work or study.
All information regarding long-term residents can be found on the website of the Swedish Migration Agency: http://www.migrationsverket.se/English/Private-individuals/EU-citizens-and-long-term-residents/Long-term-residents.html
