Regarding the means of production, after the abolishment of Weimar constitution, private owned actually meant currently in use by some individual for a rightful purpose defined by the Government. For as long as Germans were producing for the Germans, while coordinated by the Government of Germany, they were free to own their means of production. That’s the main difference between national socialists and inter-national socialists (communists). According to national socialists, bourgeoisie German is still a good German, and a Jewish worker is still just a Jew. Properties will be expropriated from Jews, and will be redistributed among Germans. On the other hand, according to the communists, Jewish worker would be a good worker, while the factory owner, although German, would be a member of bourgeoisie, thus undesirable class. This is why national socialists used to viciously fight other socialists (especially international socialists – communists), not only by using words but fists as well, and this is the reason why seemingly simple and seemingly virtuous claim that someone is anti-Nazi is actually very vague.

Here’s two of the articles of the Weimar Constitution relating to property rights that were scrapped by the decree.

Article 115. The dwelling of every German is his sanctuary and is inviolable. Exceptions may be imposed only by authority of law.

This is scrapped. Your home is no longer yours, if the State decides to take it from you.

Article 153. Property shall be guaranteed by the constitution. Its nature and limits shall be prescribed by law.

Expropriation [which is - noun, the action by the state or an authority of taking property from its owner for public use or benefit.] shall take place only for the general good and only on the basis of law. It shall be accompanied by payment of just compensation unless otherwise provided by national law. In case of dispute over the amount of compensation recourse to the ordinary courts shall be permitted, unless otherwise provided by national law. Expropriation by the Reich over against the states, municipalities, and associations serving the public welfare may take place only upon the payment of compensation.

Property imposes obligations. Its use by its owner shall at the same time serve the public good.

This was also scrapped. The State could now steal your property off you, and didn’t have to compensate you. So, by law, private property rights no longer existed. Individuals couldn't own property, since all property could at any time be seized by the state. In effect, without property rights, all property belonged to the State, and the German people were effectively ‘leased’ it by the State until it was taken off them. This is why the Reichstag Fire Decree is actually one of the first acts against the Jews - because it stripped them of their property rights, which meant that, they could have their property seized, which the Nazis later took off them.

The Germans on the other hand were allowed to keep their property because that suited Hitler and the National Socialist State’s ideology, but non-Germans, or Germans who weren’t obeying the State, could have their property or businesses stolen from them.

"The Nazis viewed private property as conditional on its use - not as a fundamental right. If the property was not being used to further Nazi goals, it could be nationalized.”

“Prof. Junkers of the Junkers aeroplane factory refused to follow the government’s bidding in 1934. The Nazis thereupon took over the plant, compensating Junkers for his loss. This was the context in which other contracts were negotiated.”

“Manufacturers in Germany were panic-stricken when they heard of the experiences of some industrialists who were more or less expropriated [had their property seized] by the State. These industrialists were visited by State auditors who had strict orders to “examine” the balance sheets and all bookkeeping entries of the company (or individual businessman) for the preceding two, three, or more years until some error or false entry was found. The slightest formal mistake was punished with tremendous penalties. A fine of millions of marks was imposed for a single bookkeeping error. Obviously, the examination of the books was simply a pretext for partial expropriation of the private capitalist with a view to complete expropriation and seizure of the desired property later. The owner of the property was helpless, since under fascism [it’s actually National Socialism, not Fascism] there is no longer an independent judiciary that protects the property rights of private citizens against the state. The authoritarian State has made it a principle that private property is no longer sacred.” 

Majestic, 5 hours long video about Hitler's socialism