I will be renting a car and traveling through Sweden and Norway this fall, staying in hotels in towns and cities overnight along the way. In general (if there is such a thing) are cars allowed to park overnight on streets for free? Or are expensive parking garages the only option for the auto traveler?
I would be inclined to search for lodgings that have some sort of parking available.
Be sure to inquire locally. For example, Bergen is a problem with cars. RS Scandinavia Guide: "Parking is difficult and costly - ask your hotelier for tips. Note that all drivers entering Bergen must pay a 25 kr toll." We stayed at a small, cozy hotel in the residential area just up the hill a few streets from downtown - very convenient for walking. Not so convenient for parking. We had to pay something like 25 NOK per day for a spot that was 5 minutes walk (uphill) from the hotel.
Oslo has a toll ring: https://www.oslo.kommune.no/english/politics-and-administration/green-oslo/best-practices/the-toll-ring/#gref
Oslo's tolls are disincentives to reduce emissions/pollution and traffic congestion, and helps pay for transit.
In recent years, significant expansions in the public transport
system, in Oslo, have been financed by a toll ring. The toll ring is
also an important tool for traffic reduction, transition to
zero-emission vehicles, GHG reductions and improved air quality.
You will need to study the Norwegian automated toll collection system: http://www.autopass.no/en/visitors-payment
All drivers, regardless of nationality, have to pay Norwegian road
tolls. The automated toll stations are all equipped with a camera that
reads the vehicle number plates and toll tags. Foreign registered
vehicles, without a toll tag, will be invoiced by Euro Parking
Collection plc (EPC).