If you don't have a Visa, I probably would not move before you do - H-1B visas are a lottery and O1 visas takes up to a year to get before you can even start working. Yes companies do conduct online interviews and will try to get you a visa before you move but it is hard.
Another route could be working for a European consulting firm or a Swedish company with an office in SF, then move to the US via them. Good luck!
Or an American company like Microsoft, Google or Apple. Those have some development done in Sweden, but you can get employed anywhere in the EU much easier than in the US, at least Visa wise, or take technical support roles and move on later to the US.
If you want a larger company, find some job postings and apply, though ideally you'd want to speak to someone at the company. And yes, online interviews are quite common.
Avoid the Bay area if you can. Its on the decline.