James Diehl's The Thanks of the Fatherland covers the German veteran situation after WWII, but it also includes a significant amount about the treatment of WWI veterans under the National Socialists.

Veterans were highly thought of by the National Socialists, though actual treatment tended to fall short of the propaganda. That propaganda tended to cast the NSDAP and SA as the "sons" or "heirs" of the army of WWI. The general idea was that these "new armies" would find the triumph that the first army didn't. National Socialist propaganda tended to emphasize the way Germans (and particularly veterans) suffered depredations under the Weimar Republic as their pensions and savings were wiped out under hyperinflation.

With so many veterans in Germany, appealing to the veteran vote was key to winning elections. This meant the idea of service, of being a soldier was set up as a shining example. Someone who served at the front was the best of all, and if you were wounded, that simply meant you had paid the price to become a "first citizen of the Reich."

Under the Nazi government, Hanns Oberlindober became head of veterans affairs. He managed an organization whose name I won't try to spell -- I'll just call it by its initials, NSKOV. Oberlindober was a keen politico and he repeatedly tried to expand the scope of NSKOV (as indeed most Nazi organizations did -- see the phenomenon of Luftwaffe field formations) without much success. It remained an organization for disabled veterans.

In 1933, Oberlindober unveiled a 12-point plan that he said would transform veterans by giving them the honor they deserved for being "first citizens of the nation." In addition to the pensions of the Weimar Republic, he proposed granting front veterans a special medal, reserved seating at public functions, preferential treatment in government offices, reduced-price tickets for trains and events, and preferential hiring (including quotas) in government jobs.

This proposal, like most Nazi grand plans, was cut back and back (a service medal did happen), and by the time it became law in 1934, the biggest thing left was the Frontzulage, a supplementary pension for everyone who had been wounded at the front. It wasn't much, and not that many people qualified for it, but the government made a big deal out of it. Hidden in the preface of the law was a statement to the effect that although the government recognized that veterans deserved more, the priority for an economic recovery meant more benefits had to wait.

In subsequent years, complaints that SA men were getting jobs reserved for wounded veterans did make enough noise that the practice of job-stuffing was limited, and veterans did get many of the jobs they were promised.

One of the biggest changes as Nazi rule progressed was the way disability pensions were awarded. Instead of determinations based on the percentage of disability (as under Weimar), the Nazi pension system was based upon how you got the wound. Was it a combat wound? How did you earn it? Someone injured in an accident behind the lines -- say, getting run over by a truck -- would get less priority than someone who suffered a shrapnel injury. In addition, length of service and rank became factors in the pension calculation.

After the start of WWII, the NSKOV became much more of an active tool in organizing veterans to take over jobs behind the front, things that might support the war effort even if they couldn't fight at the front.

I just wanna add a quick little detail and note. You should explore pre-Nazi Germany as well. It will provide insight into how veterans were treated leading up to this period. You ask what they are doing in Nazi Germany, but shouldn't you know what they were doing up until that point? How they were treated in the years prior? To get to where you are going you need to know where you have been. That might seem cliche, but I think it's a prudent question. I will lend a little bit of help toward this.

Look into the Freikorps (free corps), a lot of German veterans upon returning from the First World War had problems reconnecting with society and civilian life. I think this should come as no surprise as the First World War showed the impact of the battlefield both in the physical and psychological states of the veterans. I personally feel that Freikorp members were taken advantage of as their need for structure made them easy targets for joining a paramilitary organization. The Freikorps are known for putting down communist uprisings following the First World War.

I have to go for now. I hope this has added perspective and added a layer to your question. /u/The_Alaskan gave great direction for you as well.

Sources:

Carlos Caballero Jurado, Ramiro Bujeiro (2001). The German Freikorps 1918–23: 1918–23. Osprey Publishing.

Hitler's Heralds: The Story of the Freikorps, 1918-1923 by Nigel J. Jones