If you work permit not expired within next 90 days, then you can apply for a visa.
Sometimes they mention that you should have "permanent" residency, but what they actually mean it's residency. (It's can be temporary if more then 90 days left)
Also you should have at least two empty pages in your passport, and your passport should be valid for 6 month longer after the date when you Russian visa expired.
Contact Visa Center, they give right answers.
http://www.ifs-sweden.com/main.php?id=contact1&lang=en
+46 844685054 (Mo – Fr from 09:00 to 12:00, from 13:00 to 17:00)
They also accept documents by post.
What you basically need:
- tourist voucher or invitation.
You can buy it online from many different Russian visa support sites,
for Europeans it's cost from 5 EUR, for Indians from 10 EUR.
Usually issued instantly and it's already confirm that you have place to stay for all period of visa.
You can also obtain invitation from a hotel, Russian citizen or from a Russian company.
- Insurance (Just UK, USA citizens and may be few more who don't need it)
Exactly in Stockholm they super strong about the insurance. They don't accept copies, it should be an original insurance with real stamp and signature.
I usually buy insurance in Russia, as they cheaper there. For example for 1 week, it's cost 4 EUR. with a cover for 30 000 EUR. (as required for visa). When I applied with such online issued insurance they refuse my application in Stockholm, I contacted consulate and proved, that other embassies accept it, and it's completely suits to their requirements. After two weeks of corresponding with me about this matter, they start to accept online issued insurances too, but may be not from any company yet. I applied with AlfaStrahovanie online insurance, and they accepted it.
- Visa Application.
When you have tourist voucher or invitation and insurance you can fill the application form for visa.
https://visa.kdmid.ru
In the end, when they ask to choose where you going to apply, I would recommend to choose "Visa center, Stockholm". (http://www.ifs-sweden.com)
- Picture 3.5 x 4.5
Reed more about requirements here:
http://www.ifs-sweden.com/main.php?id=travel&lang=en
Sometimes Swedish apply for Russian Visa in Finland or Norway instead, as it's easier to get it there, but you can do it only in Sweden, as you have work permit in Sweden.
P.S.: I do first three steps within 30 minutes :)
I have experience to prepare documents for visa for my Chinese (which counted in Russia with even bigger immigration risk than India), Korean, Swedish, Japanese friends for Russian embassies in UK, Norway, Sweden and Japan.
If it works for Chinese with study permit, must work for Indian with work permit too!