For the sake of time I will post links then try to summarize each one.
Austrian -
http://en.wikipedia.org/wiki/Austrian_School_of_EconomicsBasically Lassiez Faire, Gold Standard, and Free Trade. Liberal and Libertarian in a modern sense.
German -
http://en.wikipedia.org/wiki/Historical_school_of_economicsFor the most part rather then being a set philosphy it was more about scientific approach to studying the economy. None the less many of the people who promoted this often tended to be more Economic Nationalist, Protectionist, often defended Trade Unions, and advocated much more Gov't involvement in the Economy. I would guess that since every Economics Professor in Germany was brought up under this that the roots of fascist economics are found in this school. Ironically they strongly Influence US economic policy in the late 1800's cause several German Economists emmigrated here. It mostly dealth with Trade policy though. European Social Democrats of today may also take some influences from here. Conservative, reactionary, and some forms of modern day socialism.
English -
http://en.wikipedia.org/wiki/English_historical_school_of_economicsSimilar to the Germans in that they wanted to return to Inductive reasoning instead of the Deductive reasoning used by the Classical and Neoclassical Schools. They were also similariy Protectionist and viewed classicalists as defending Free-trade in an imperial and colonial setting where it is out of place in there view. Other then that there were not as Interventionist as the Germans. Probably the same as Germans.
Marxian -
http://en.wikipedia.org/wiki/Marxian_economicsPure and simple old fashioned Communism.
I am tempted to include Keynes but I want to keep it between about 1850 and 1920 and force you to choose between the four that are up there.
It is also late and I am getting tired. Ideological labels are in a standard Global sense not US or 21st century specific.