Logistically it would've made more sense to fly into Helsinki, or even St. Petersburg and out of Oslo, but if it's all confirmed then you'll have to pay a significant amount more for internal transport.
To me, the most interesting city on that list is St. Petersburg, but the visa costs and hassles will be a hindrance that you might want to avoid if you're only planning on doing 3 days there.
If you're playing tourist, you'll only need 2 days max in all of these places to see the sights. Helsinki is pretty much a one (long) day city, as is Oslo. If you really need to get laid, I'd only do 2 cities and pipeline hard.
It's worth mentioning that girls in these cities work and do shit, so they're not going to be eager to meet during the week. I'd try to position myself in the city with the biggest population and most sites of interest during the week and the smaller cities like Helsinki and Oslo for the weekend. Kind of like how NYC will be way easier on a Tuesday than Atlanta.
I spent a week in Helsinki and regretted it for 2 reasons - one, because I got the flag my first night there - albeit a very average girl, and two because there wasn't much to do there besides getting wasted on the weekend. Lots of average girls on Tinder that are eager, but the stunners won't be lining up to meet you online.
Here's how I'd do it:
- First start in Helsinki, assuming it's the weekend. Stay within walking distance of the Main Station.
- Book a SAS flight to Copenhagen and route it through Oslo with an 8 hour layover so you can see The Scream. Here's an example of what I mean through a Google flights link:
http://goo.gl/flights/WJAU
- 2-3 days in Copenhagen, fly to Stockholm for the weekend (SAS is better than Norwegian fees-wise unless you travel very light) Looks like $66 one-way.
- Weekend in Stockholm, lots of drinking and partying and slutty women. Estimated cost: $400 w/accommodation.
- Fly back to Helsinki and hope that you don't have to cough up another $100 for a night to make your flight and can do it in the same day.
You can also finish in Helsinki as well, which might be the thing to do if you have an early morning flight out of HEL. In that case, fly to Stockholm directly after landing and do the OSL stop on the way to Copenhagen before returning to Helsinki for the weekend.
Another tip is that SAS offers youth fares, which are really great deals for last-minute travel. You have to be under 26.
SAS Youth Fares
Good luck!