I'm sure this has been asked before, but we will be flying from Milan to Stockholm (with a quick plane change in Oslo) and was wondering if we have to go thru customs / immigrations upon landing in Stockholm. I know European countries have agreements within the EU, but not sure if Sweden is included in this. Also, we will be heading to the Abba museum, has anyone taken an Uber from the airport to the museum? Thank you!
It has nothing to do with being in the EU, but within the Schengen area. Since Sweden and Italy are both within it, you won't have to worry about either Immigration or Customs.
All three countries are part of the Schengen agreement, so as stated, no formal immigration or customs. However, as you board or earlier through security, you will need to show ID (your passport).
If you really want to be technical though, when you land in Norway, you are still in a Schengen zone, but out of the EU. You will be "airside" so not entering Norway, but if you were, technically you would need to go through Customs, once in Sweden, neither applies.
If you do an internet search for "eu schengen diagram" there are any number of nice charts that help make sense of which country participates in which European program or organization.