I'm going to Sankt Peter-Ording for a wedding. Where else should I go?

Sankt Peter-Ording is in Germany. 
>I was thinking of trying to swing through Denmark, Norway, and Sweden. Is this viable? 
It is theoretically feasible (see below) but imo rather pointless trying to see 3 separate (and very different) countries, each with its own currency,  in only 5-7 days (and possibly less...see below). Unless you just want to 'tick boxes'?
You don't say whether you have bought a round-trip ticket or are still able to organise an open-jaw ticket. I'm going to assume round-trip, so that limits your time even more because you'll use up at least one of your days getting back to your departure airport.
You could of course just nip from capital to capital by air. It will take time, it won't be cheap and you won't see much of any country unless you make at least one daytrip (train or bus) from each capital. No European capital city accurately reflects the rest of the country.
www.skyscanner.net will give you all flights and fares from x to y on your dates. Book on the airline's own website.
If you are set on 3 countries the best way to maximise what you can see is to use the railway  (I'll give links below). Perhaps overnight in Odense , then visit Roskilde on the way to Copenhagen.  At least one overnight there then take the train over the magnificent Oresund bridge to Malmo in Sweden. You could overnight there and/or take the high-speed train to Oslo with an overnight before making the return trip by overnight ferry to Copenhagen and train back to your departure point. 
Official railway websites (all in English):
Germany    https://www.bahn.com/en/view/index.shtml
Denmark   https://www.dsb.dk/en/
Sweden   https://www.sj.se/en/home.html#/
Norway  https://www.nsb.no/en/frontpage
Oslo > Copenhagen ferry https://www.dfdsseaways.co.uk/ferry-routes/other-routes/ferries-to-denmark-norway