I might tweak it just a bit, but you are definitely on the right track for an interesting 2 weeks.
I would spend no more than 2 full days in Iceland, the 1st being the day you land (most flights land in the early morning). There are many organized tours that take you to groups of top sights in that SW corner of the country, each lasting 6-10 hours. Two of those tours and you have pretty much seen 90% of what there is to see. Or take one tour and spend the rest of your time wandering central Reykjavik (worth about 6 hours, tops). The IHY youth hostel there is great and has a thermal public pool nearby.
If you land in Bergen next (mid-day), the rest of that day and all of the next is plenty of time for Bergen.
The nutshell is a very long, full day, but well worth it.
Oslo in 2 full days is perfect.
I don't know anything about Gothenburg, I'm afraid, but it's not that far en route to Stockholm so maybe an early departure from Oslo would get you there with 2/3rds of a day left, then 2/3rds of the next day, then take an evening train to Stockholm.
3 days in Stockholm is perfect.
I think I have saved you about 2 days with my suggestions and with that time I would do one of two options;
1) Spend those two days doing a more elaborate Norway fjord experience than the "quickie" nutshell. I could offer some suggestions if you are interested...
2) From Stockholm, take the fun, beautiful and economical overnight Silja ship to Helsinki and either stay a full day there and fly home open jaw from Helsinki (we did) the next day or just stay the day (10AM-5PM) and take the ship back to Stockholm for your flight the following day. Helsinki is nicer and more interesting than people think. It's also off the beaten track a little so you can enjoy seeing a great city 99% of Americans will never see.
I can also endorse specific hostels for Stockholm and Helsinki if you are interested. PM me.
