Actually, we still need an explanation to why they waited until mid day before they left Stockholm. They could have left already the night before, when Eli could have travelled openly in the darkness of the night.
I have thought about this a lot.
The only reason that I find believable is that Oskar wasn't ready to commit to a life with Eli until late in the morning of the 13th. Then it suddenly became urgent - if not, they could have waited until the next night and avoided the hassle with the trunk.
This is what I think might have happened:
When Oskar was pulled out of the water he was too worn down to feel anything. He barely noticed that Eli had returned. Eli helped Oskar to dress and to leave the bath house.
Eli's first assumption was that Oskar would want to go to his mother, since that is what Eli himself would have wanted. So Eli led Oskar to his apartment door. But Oskar didn't want to enter, to Eli's astonishment.
At the apartment door Oskar realised what was about to happen, and mustering the little power he had left he led the way down into the basement, into the storage compartment that belonged to the apartment. There Oskar and Eli spent the night. Being exhausted, Oskar soon fell asleep and then slept through the night. Maybe he didn't sleep well, perhaps he had nightmares, and Eli comforted him. Still, Oskar slept most of the time until morning.
In the morning of the 13th Oskar finally woke up. He now was less tired and numb than the night before, and was able to think. However, he didn't immediately decide to go with Eli. Something held Oskar back. What?
Maybe the thought of leaving his mother, which he surely knew would be the most cruel thing he cold do to her.
Maybe the thought of having to kill people. The experience in Eli's bathroom would have made a strong impression on him. He would still remember the look in Lacke's eyes.
But if he didn't go with Eli he'd never be happy again. The last three days had proven that.
What to do?
I think it would have been a very hard decision. Oskar might have pushed it away, tried to avoid it, for several hours.
But eventually Oskar made up his mind. Perhaps the tipping point was when he realised what danger it was for Eli to be with him in the basement. Perhaps Oskar realised that the police would search for him, and that they would look for him everywhere. Eli wasn't safe with him in the basement. Suddenly time was becoming short. Eli had to be saved.
The choice had been made. Eli crept into the trunk, and Oskar took it to the railway station via the underground train.
When the train started rolling and Oskar was able to relax, he found that he was happy.
So, where did Oskar get the trunk? Well, the most likely place would have been in the storage compartment. It was an old heirloom of Oskar's mother's. Why complicate things?

