The short answer is yes, in Sweden your boss can ring you while you’re not working, but in practice it's a bit more complicated.
There's no ban on them calling or emailing you, but they're not allowed to legally require that you answer the phone or reply to emails outside of work hours.
This means that you’re perfectly within your rights to not pick up the phone or check your emails while on holiday or when you’re not working.
Essentially, you’re either carrying out work, or you’re not. Your boss can’t expect you to answer outside of working hours, and they can’t put you on standby while you’re legally on holiday either. You are allowed to answer emails or phone calls if you want to, or if you’ve agreed to do so in advance with your boss, but that’s your own choice.
In certain professions, it can be difficult to switch off or know exactly when your boss expects to be able to get hold of you. In this case, it might be good to ask if they have a nåbarhetspolicy (literally a "reachable policy") with specified times where they expect you to answer calls and be available. If they don’t have one, ask about setting one up. Your union will probably be able to provide you with an example policy.
If you're not on a full-time contract and want to work extra shifts, your boss is allowed to contact you on your time off to offer you shifts or days working. Again, you don't have to answer, but it might be in your own interests to do so.
What if my boss asks me to come into work when I’m on holiday?
In this situation the exact wording used is important. If your boss asks if you would be available or willing to work while you’re on holiday, you can say no. If they order you (beordrar), then you have to come in and work.
There are some legal requirements in this case, too. Your boss has to prove that they tried every other possible route before asking you to come back into work while you were on holiday, and they also need to cover any costs you incur by doing so, such as extra flights or the cost of a hotel which couldn’t be refunded, for example. In some cases, you’ll be offered extra days of holiday too.
Obviously, your boss can’t do this if they can’t get hold of you. There is no penalty for you as a worker if your boss calls you to try and get you to come into work and you don’t pick up during your time off.