For Munich, almost everything people generally go to see, except Dachau, is in the inner zone. Dachau, however, is in the Munich Metro District, MVV, so an MVV ticket is what you need.
A day pass for your group for the inner zone is 12,80€. An inner zone group pass for three consecutive days is 28,00€. If you want unllimited travel in the inner two zones, you'll want a Munich XXL group day ticket for 15,40€/day. If you want to go out to, say, Freissing, to Weihenstephan, the world's oldest brewery, to the Spa in Erding, or to the airport, you will nead a pass for the entire network, at 23,20€/day. These day passes are valid for all modes of transport (S-/U-Bahn, trams, and buses) of the Munich transit district.
Here is the map of the system with zones shown. Here is the table of prices for group day tickets.
For either Neuschwanstein or Regensburg, both of which are in the state of Bayern (Bavaria), a Bayern-Ticket for four people in 2nd class at 38€ is what you need (1st class is available for a higher price). You can only use regional trains with a Bayern-Ticket, but that's about all there are to Füssen (Neuschwanstein), and regional trains (RE and ALX) are the fastest way to get to Regensburg. You can only use the Bayern-Ticket after 9 AM on workdays. The Bayern-Ticket is also valid for all modes of transport in the MVV and the Regensburg metro area that day.
If you book far enough in advance (92 days, max), you (all 4) can get from Munich to Strasbourg for as low as 156€. I saw that fare for one day on the ICE leaving Munich at 8 AM; 196€ or 236€ are more common for that route. That is using a SparPreis ticket that is train specific (limited for use on only a single train per leg on that date). It can only be refunded or exchanged with penalties.
If you don't mind taking regional trains, slower (7 hours vs 3¾ hr for the ICE above) and more changes, you can use a Quer-durchs-Land-Ticket for 68€ for the four of you or, only on weekends, a Schönes-Wochenende-Ticket for 52€ for both of you. Those tickets can be used on any regional train and don't require advance purchase. They will get you as far as Kehl, across the Rhein from Strasbourg. A local ticket for the rest of the way would cost 16,40€ for all four of you.
About the fastest way to Diersheim is to take the train back to Kehl (you already know that fare) then take the #430 bus, about 20 min, to Diersheim. The bus from Kehl to Diersheim costs 3,20€ per person, each way. There is about one trip per hour.
According to the Bahn, taking all regional trains from Strasbourg to Freiburg is only about 20 min slower that taking an ICE from Offenburg to Freiburg. You can use a Baden-Württemburg-Ticket (38€ for the four of you) to get from Kehl to Freiburg.