Originally I planned to do all my travel by train but now I’m thinking it would be a lot easier and save time and hassle is if I rent a car on my way out of Munich until I get to Salzburg. In between I’m staying 2 nights in Fussen and one night in Oberammergau. I plan to stop in Innsbruck on my way to Salzburg but not stay the night. My main concerns are picking up the car in Germany and dropping it off in Austria. And parking in Oberammergau during the Passion Play.
I've spent almost 4 month traveling in Bavaria, mostly by rail, some by bus, a few short taxi rides, never by rental car. I know that, in most cases, a car is not necessary to get around in Bavaria.
The rail lines in southern Bavaria mostly radiate out from Munich, particularly to the south, so it is often difficult to move east to west (or v v) by rail, but the rail system in Bavaria is heavily augmented by a system of buses, most notably by the Regional Verkehr Oberbayern (RVO, www.rvo-bus.de). The RVO website is in German, but the Bahn website will show RVO bus connections (although not fares).
Here is a map of the extensive system of buses linking towns in southern Bavaria.
I know that there are bus connections from Füssen to Oberammergau (I've been on one, albeit the other direction). Most connections have one quick change at Echelsbacher Brücke.
You can get from Oberammergau to Innsbruck via Garmish-Partenkirchen and Mittenwald. From Oberammergau there is either rail connection through Murnau to GaP or a direct bus that makes a stop in Ettal. From Innsbruck, you probably want to take an Austrian Rail RailJet that goes through Germany (Rosenheim) to Salzburg without stopping.
If you do want to rent a car and leave it in Salzburg, there is a Europcar rental office just across the river in Freilassing, Germany, so you don't have to leave the car in Austria.
You can turn in the car just across the border from Salzburg in Germany
Yeah, it's right at the intersection of Salzburger Strasse and Ludwig Zeller Strasse in Freilassing. And near there is a bus stop for the bus that will take you into Salzburg. If I remember, that bus goes into the old town, under the fortress, not to the train station. Or, if you have all your stuff with you, and you are going back to Munich to fly home, it's a short walk (½ mile) to the Freilassing Bhf.
My wife and I also rented a car on the way out of Munich for a few days in Bavaria. I would definitely recommend it. It gave us the freedom to take some smaller, lesser traveled roads to our destinations, and to pull over for 5 - 15 minutes if we saw something we wanted to check out or photograph (oooh, look at those cows grazing with the lake and the Alps in the background!). Or see something like the Wieskirche near Steingaden (between Oberammergau and Fussen).
And I got to drive 100mph for the first time in my life (for about 5 seconds, still being passed) on the autobahn out of Munich heading to Oberammergau. Check.
As far as parking, your hotel/inn in Oberammergau should be able to help. Many other guests will surely arrive by car and the hotel will have a plan for you. We didn't have any trouble parking in any of the small towns during the day stops. Good ideas above about dropping the car in Germany.
And I'll never forget popping the clutch in a traffic circle and stalling the car while still in Munich, and not how to restart the car. (They had the car running for us when we picked it up 10 minutes earlier.) 60 seconds seemed like 30 minutes. But it was a weekend morning, and the Munichers were kind enough not to curse us as they maneuvered by. My point is, every time we've rented a car in Europe, we ended up having some kind memory related to the driving adventure that we could look back on and laugh.
Thanks for the tips. I'm still torn about which I want to do but its good to know both are viable options.
One other consideration to think about if driving in Austria with a German rental car is the Austrian highway Vignette, It doesn't cost too much, around 10€ for 10 days but you need to get it before crossing the border on a motorway (enforced by cameras at the border and after) although it is not required on back roads. Failure to display it correctly or have the appropriate electronic one results in big fines.