Oh cheap air travel, here I come...

Academics and legal matters aside, you need to prepare for living in a new country and also need to find the cheapest way of getting there right?
I can't find a ticket for you and we can all do this ourselves, but I can give you a few pointers.
First of all, if you are going to be studying in Jönköping, I would 100% recommend that you fly to Gothenburg. I'm sure you've heard of Stockholm (being the capital), but if you haven't heard of Gothenburg, it's the 2nd or 3rd largest city in Sweden and more than likely this will be your point of entry. It is much closer to Jönköping (2hrs compared to 5 with Stockholm) so not only will arrive sooner, but it will save you a lot on transportation costs.
Here's a website I use very often to book trips. You have to register and verify your student status, but it will have many cheap flights to any place in the world.
Of course, you can use all the other online agencies like Kayak, Cheapoair, Skyscanner, etc...

I would also try seeing if it'd be cheaper to buy separate one-way tickets; it's very unlikely, but it has been less expensive in some cases.
I wish you the all the luck in finding the best least costly flight!!

I would try to book in advance and you can find round trip tickets as cheap as $750-800, but if you procrastinate it can easily reach past $1200