Upvote:3
As a Vietnamese citizen, you need to obtain a Schengen visa (a normal transit visa) in order to transit through Stockholm.
There are two kinds of transit, airport (airside) transit and a normal transit. You need to normal transit visa since you need to enter the country, collect your bags and then board your next flight.
The airport (airside) transit visa is for those passengers that are coming in from outside the Schengen zone, and are transiting (changing planes) to continue their journey. Usually these travelers are on a single itinerary (ticket) and do not have to collect their bags.
Once you have this visa, you can stay at the airport, or at any hotel / accommodation in Stockholm till your next flight.
Upvote:6
I do not understand the problem but let's break it down. I presume you do not want to check into a hotel at Stockholm but rather want to wait it out in the transit area. I will presume you are a citizen of the United States. If this is not the case, things get more complicated. Citizens of the US are exempt from Schengen short stay visas so you are welcome to stay 90 days (out of any 180) in the Schengen area and so 1-2 days at the airport is just fine. Here's the sleeping guide to Arlanda.
Passengers who are not visa-exempt under the Visa Waiver Program and travel from the U.S. (or any other non-Schengen country) via the Schengen zone to another non-Schengen country do not need a visa if they do not leave the transit area of the airport. I do not know but I believe you are allowed to stay 48 hours in transit.
Edit: now we know that OP's question is a totally different situation as the important flight is ARN-ATH. That's an intra-Schengen flight and as such you are entering into the Schengen zone and you need a Schengen short stay also known as "C" visa. The other flights, one tickets or two tickets are just distractions and do not matter.