"Renting a car - I heard that it was cheaper/ more efficient for 4 people?"
Sounds like "they said ...". Who are they? I've been traveling in Germany for 15 years, and I've never found a car to be cheaper. The car rental quotes I get are always for a compact car, suitable for at most three people with moderate luggage. For 4 people with only a little luggage, you need at least a family sedan and rental costs and fuel will be more.
I think the people who say a car is cheaper for 4 don't know how to buy train tickets. I've found that for me, with 1 or 2 people, a car is 2 to 3 times as expensive as using trains, and extra people are not that much extra. For example, a Schönes-Wochenende-Ticket (valid for travel through Germany on weekends) is the same price for up to 5 people. A regional ticket, like a Bayern-Ticket or a three Länder (Sachsen, Sachsen-Anhalt, Thüringen) Ticket is usually only 4€ for each added person (2-5). A Quer-durchs-Land-Ticket, valid throughout Germany on weekdays, is only 8€ more for each extra person. With sufficient advance purchase, a Savings Fare Ticket, for express trains, is 10€ to 20€ more for each person.
For example, Quer-durchs-Land tickets for Konstanz to Oberstdorf, the closest place to Konstanz where you can hike in the German Alps, would cost 68€ (44€ one a weekend day). ViaMichelin estimates the cost just for fuel for a family car as 28€. On top of that, you'd have the car rental for a day. The Bahn schedule shows the trip taking 3hr 31min. ViaMichelin estimates the driving time at 2hr 56min if you go through Germany to avoid needing to buy a Swiss vignette.
For Oberstdorf to Erfurt, ViaMichelin says 5hr 10min and 76€ just for fuel. With sufficient advance purchase, you can get train tickets for a 7hr 10min trip for 89€.
Once you are in the Luther area, you can travel all day with a Thüringen-Ticket for 34€ for all four of you. This would include all regional trains and most bus lines. Erfurt to Leipzig to Wittenberg would cost you 35€ just for gas for the car. On the day you stay in Wittenberg, the car would probably sit idle but still cost you a day's rental. So far I'm seeing just fuel for the car costing about the same as train tickets, but there's the cost of renting the car and insurance on top of that.
If you go from Wittenberg to Berlin on a weekend day, use a Schönes-Wochenende-Ticket for 44€; on a work day, use a Thüringen-Ticket for 34€ to the border and a 29€ Brandenburg-Berlin ticket the rest of the way, including local Berlin transportation to your hotel.
Of course all trips are different. You should definitely do the comparison yourself, don't just go by what "they" say.