I don't know much about the Italian Blackshirts, but the SA I do know quite a bit about.
The SA had many roles, street fighting was just one of them. They attended NSDAP functions (rallies, meetings etc), assisted in the paperwork and administration of running the party, put up posters/handed out pamphlets, assisted in the various social programs (food distribution, training the Hitler Youth etc) and much more.
When it came to combat, most violence would occur during big elections when rival National Socialist and Communist rallies came in contact with each other, SA and the various commie paramilitaries brawling in the streets. Physical control of the streets was a big factor in who had power in Germany (for example, see the massive campaign where SA were bussed in from all over Germany as a physical presence to break red Berlin). Raids against opposing political hangouts (bars, meeting halls, clubs etc) to keep them from organizing and discourage participation in them were common as well, the SA having it's own specialized unit (The Rollkommando) of motorized masked men who would roll up to a communist nest, storm in beating the shit out of anyone with clubs and trash the place.
It went far beyond brawling though, especially from 1930-1933 with the great depression. Assassinations, shootouts, bombings and murder were prevalent and the situation nearly boiled into open civil war several times. The Berlin police commissioner received no less than 10 reports of violence involving the NSDAP daily when it was at it's worst. It only subsided when Hitler took power and all the commies either fled or got camp'd.
The SA used a military model for their organization, having military ranks, specialized corps (engineers, signals, infantry, medical etc), organizing themselves into battalions with a dedicated fighting company. Rohm even put forth the idea of the SA replacing the Wehrmacht as Germany's standing army (considering they had 3 million members at their height and the pre-Hitler army at 100k). In the interwar period, it seemed like social-democracy was dying and from it's ashes would arise either Communism or Fascism, so in Germany both attempted to build states-within-states to grab power when democracy finally collapsed, and the NSDAP was far more successful in this than the Communists (who relied more on foreign, Soviet support).
Today cell structures (small groups operating independent of one another) would be far more appropriate for organizing. The NSDAP had a degree of public acceptance that allowed them to have a more open presence in Germany, the same is not true in America today, we are the system's #1 threat ultimately and they have and will use any methods to break up anything truly serious. Infiltration, monitoring, bogus charges, outright murder are all possible if you're truly dangerous and truly commited.
(cont)