Will I need a visa to travel across Europe?

I think you will need a Visa. My Chinese friend has residency permit in UK for 5 years but cannot go to Europe.
 
Maybe. Sweden is part of the Schengen Area, a group of countries in Western Europe that have eliminated border crossings between themselves. If you have a Visa valid to enter and stay in Sweden that should let you travel around to most of Europe (but not the UK). That said I would recommend contacting the Swedish embassy/consulate in your country and ask if you permit will allow you to travel to other Schengen countries.
 
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