For an American, staus are defined as a lack of movement on the autobahn, or marginal movement.
For nine months out of the year.....staus occur and are of an acceptable level. Either because of accidents, ice, snow, or construction...Germans will get into a normal stau and just accept the fact that a 90-minute ride turned into 140-minute ride or worse.
The summer period is different.....these staus are monumental and epic in some ways. There are Germans who will boast they were in such-and-such stau in 1981 that twisted a four-hour trip into twelve hours.
What triggers the massive summer staus? There's a certain period when summer vacation periods start up with kids....which relates to vacation movement by car....by millions of Germans. Add in the fact that there are least two significant autobahn construction projects always underway and limiting traffic flow greatly. Then toss in rain or thunderstorms.....to create accidents, which limit movement.
The typical German response is to quickly find an alternate route.....usually on a two-lane road and hope to get around the "mess". If you do this early on in the stau.....it usually works. If this is hour two of the stau....the secondary roads are clogged and just as bad as the problem you originally encountered.
So, my general advice.
If you travel in the summer months....consider leaving early in the morning (6AM), and getting off the autobahn by 10AM. Most of the massive staus occur in the middle of the day. Or get onto your trip after 4PM.
If you get some hint of a stau ahead of you by 10 KM....consider just getting off the autobahn....finding a restaurant, and taking a good long two-hour lunch.
Taking an alternate route? Once you asses the one single best alternate route.....I'd quickly look near it for a second and longer alternate route that is a bit out of the way (maybe adding two hours onto a trip anyway).....just to be moving and avoiding the sit-and-pause situation of the autobahn or your first alternate route.
Days of the week better? Sundays are typically better because there's the German law forbidding truck traffic from sun-up to sun-down. Friday afternoon is usually considered the worst time of the week for possible staus....from 2PM onto 8PM. This is when Germans usually pack the bag and make a run to their vacation destination. All day Saturday....is considered the second worst period in the summer to travel.
Possible for the entire autobahn to be shut down for hours? Yes. There are epic stories about these type situations.....where no one moved for four to twelve hours. It's rare, I admit. This is the reason why you want to have an adequate water supply in the car as you start some big trip in the summer. Think beyond just one small bottle of water per person.....I'd throw a six-pack of the liter-size water containers into the car for good measure.
My own worst story? Years ago, I was talked into a Denmark vacation....to drive from Kaiserslautern up to a Danish village about an hour across the border....on a Saturday in July. I started this trip around 6AM, and if you figure the computed drive on a perfect day, with an hour for lunch and four short pauses in the trip for toilets or gas.....I should have made the whole trip in an eleven hour trip. Well....toss in the four various staus that I ran across from Frankfurt to Hamburg, and it turned into a fourteen-hour trip.
Patience? It is the key to getting through a stau, and it helps to get off the road and mentally rest for a while. If nothing is moving....don't allow the mess to screw up your patience and you start to get aggressive. Don't turn the bad stuff into something much worst.