Was there any knowledge of the camps among fighting soldiers? Did they know full on, or were they maybe only a rumour?
First of all, sorry for my English, I'm not a native speaker.
The answer is: Yes, they knew about it. They knew about the mass killings and they knew about the camps.
There are recordings of Wehrmacht soldiers (in POW camps) telling each other about mass executions, about their "exhaustion" from shooting people (especially children), about gas vans (http://en.wikipedia.org/wiki/Gas_van) and about the mass burnings of corpses. SS officers often invited Wehrmacht soldiers and even civilians to spectate mass shootings.
For the involved it was forbidden to talk about the camps and the mass killings, but there were lots of witnesses. Military units where often stationed near camps and you can find photographs of killings and abuse in private photo albums, made by Wehrmacht soldiers with their cameras. Furthermore the tracks of the trains the soldiers on home leave took to get from the Eastern front to Germany ran right next to concentration camps. Wehrmacht soldiers knew about the camps.
If you wonder if the population of Germany knew about the camps, the answer would be yes, too. Soldiers on home leave would talk to their families about it. The personnel operating the trains filled with Jews, Gays, Sinti and Romanies, and other "unwanted groups" headed to the concentration camps were no soldiers. They were able to tell their families about it.
There were other civilian witnesses too. For example the ovens and also the exhaustion systems for the gas chambers in Birkenau and Auschwitz were installed and maintained by a company from Erfurt, 'Topf und Söhne' (Topf and sons). They were in the camps during construction and saw the blueprints. They were also there during the operation of the camps to maintain the systems.
Deportations in Germany took place in public. The orginary train stations were used and often large numbers of onlookers were present. Although the Nazi government officially talked about "Umsiedlung" (relocation) or "Evakuierung" (evacuation) of the Jews, we have proof in form of diaries that people knew or at least suspected what was going on. Let me cite one entry:
"In Scharen tauchen die Juden unter. Furchtbare Gerüchte gehen um über das Schicksal der Evakuierten. Von Massenerschießungen und Hungertod, von Folterungen und Vergasungen." (Jews are going into hiding in large numbers. There are terrible rumours about the fate of the evacuees. About mass shootings and starvation, torture and gasification.)
This is taken from the diary entry of the 2nd of December 1942 of Ruth Andreas-Friedrich, who was a German resistance fighter.
A bishop, Theophil Wurm, wrote in a letter in September 1944: "Jedermann weiß oder kann wissen, wie das Dritte Reich mit den Juden verfahren ist [...]." (Everybody knows or would be able to obtain knowledge about what the Third Reich did to the Jews). He continues to write about the murders on the disabled and the ones with mental disorders and also about concentration camps.
From June 1942 onwards the BBC was broadcasting News about the concentration camps and what would later be called the Holocaust in German language.
It is important to note that although the Germans knew about mass killings and the camps, most historians agree that they did not know about the systematic gasification and the industrial nature of the mass murder. This ignorance is not attributed to the effectivness of laws or restrictions prohibiting the spread of knowledge but more to turning a deaf ear to the very obtainable facts. Industrial mass murder was hard to believe, although a study from 2007 suggests that around summer 1943 the majority of Germans anticipated that all Jews were about to be killed.
I hope I could answer your question.
Unfortunately I am unable to recommend any English literature, I'm not very familiar with English research on this topic. If you happen to be able to read German I can recommend you the book "Davon haben wir nichts gewusst. Die Deutschen und die Judenverfolgung 1933-1945" by Peter Longerich. Longerich is one of the leading Holocaust reseachers and currently working at the University of London.
Otherwise, maybe some other redditors are able to recommend something suitable.
I hope one of these can answer your question:
Was your average Nazi aware of and complicit in the atrocities of the Nazi regime?
How high ranking/connected did a WWII German soldier have to be, to know about the holocaust?
As always, further discussion and new answers are welcome and appreciated.