The legality of the SA and other paramilitaries varied during the lifespan of the Weimar Republic. After the crises of the early 1920s and the experience of paramilitaries including the NSDAP's SA, the government passed various laws designed to restrict the operations and dangers of paramilitaries. The 1922 Republikschutzgesetz (law for the protection of the Republic) introduced widespread gun control with the aim of reducing the viability of paramilitaries as a means to undermine the government. Under the rubric of "endangering public safety," the Republikschutzgesetz outlawed the organizations from owning unauthorized weapons, the creation and brandishing of a weapons arsenal, and criminalized the failure to report on the existence of weapons arsenal. These and other laws helped to stabilize the political scene in the mid-1920 and reduce much of the power of paramilitarism.
But having laws on the books and enforcing them are two different matters, and the Weimar justice system skewed very much in favor of right-wing extremism. Both police investigations and justice ministries pursued right-wing violations of the law with the same fervor that they did with left-wing groups like the KPD's Rote Fahne. Hitler's famous slap on the wrist for the Beer Hall Putsch was only on example of this judicial bias in action. At the apex of government, the conservative camarilla around Hindenburg did not really see right-wing paramilitaries as an existential threat, but rather a force that could and should be tamed. In 1929, the government enacted a wide-spread enforcement of a ban on paramilitaries, explicitly targeting the KPD and SPD's formations, but left the SA and Stahlhelm alone on the grounds that their membership was dependent on being members of the NSDAP and DNVP respectively, and thus breaking up these paramilitaries would be a violation of the Weimar constitution. The questionable legal logic of this decision was that suppressing the SA and Stahlhelm would be directly attacking a component of a legitimate political party.
This lax attitude towards paramilitaries allowed this type of violent political culture to entrench itself inside urban neighborhoods. Even though Republikschutzgesetz denied them firearms, truncheons and other sorts of weapons of the like were destructive enough for the street brawls. This urban street culture of violence made it even harder for Weimar police to actually restore order and enforce even existing laws against vandalism, assault, and murder. As street violence associated with the SA spun out of control, the government extended the ban to the SA in 1932, but by then it was too late. The ban was easily evaded, sometimes by wearing insignia inside out, and other laws like the proscription on uniforms was easily evaded or difficult to enforce. At the very least, the political violence committed by the SA was illegal, but the mechanisms to enforce it were quite weak prior to Hitler's assumption of power.
Once the NSDAP was in power, it soon gave the SA a legalistic gloss that sanctioned it not as a paramilitary arm, but as an organ of the state. Göring as Minister-President of Prussia, a position with wide-ranging powers over the police, deputized the SA and Stahlhelm as Hilfspolizei (auxiliary police) in February 1933, a move that ushered in a wave of political terror and rounding up people for protective custody. One SA Gruppenführer in early July 1933 painted a stark picture of events:
Everyone is arresting everybody, bypassing the prescribed official procedure, everyone threatens everybody with protective custody, everybody threatens everybody with Dachau.
The above quote shows how SA's actions in this period renders the question of the SA's legality is somewhat moot. In theory, they were operating as an auxiliary arm of the legitimate German government, but they were not operating in any manner consistent with the spirit of those laws that gave them this power. The early period of legal and extralegal terror caused some alarm even in NSDAP circles, most notably the Minister of Interior Wilhelm Frick, that some order needed to be restored. The ascent of the SS in its control over extralegal and legal terror was in no small measure because it promised order and to place political violence out of sight.
This sorry tale underscores the fragility of law and legal codes against political forces determined not to play by the rules. The German emigres Ernst Fraenkel and Franz Neumann produced a very perceptive analysis of the Third Reich's relationship to the law. Both men wrestled with the question of how a dictatorship and Fraenkel discerned two types of states at work in Germany: the prerogative state and the normative state. As they explained in their book The Dual State:
By the Prerogative State we mean that governmental system which exercises unlimited arbitrariness and violence unchecked by any legal guarantees and by the Normative State an administrative body endowed with elaborate powers for safeguarding the legal order as expressed in statutes, decisions of the courts and activities of the administrative agencies.
In The Dual State, the NSDAP and its organs are the prerogative state writ large; concepts like Führerprinzip (authority flows from Hitler), the primacy of ideology and action over rational thought (as Mussolini said "it does not matter what you think so long as you obey!"), and other aspects of fascism allowed preexisting aspects of the prerogative state to expand an colonize other components of government and society. Legal norms and structures have to be twisted around prerogative state's ends and these ends could often shift. This explains some of the chronic dysfunction of the Nazi state, but also its propensity towards violent solutions as a means to cut various Gordian knots. The Wannsee Conference illustrated this in that one of the few discordant notes during the Conference was the SS's intention to violate the Nuremberg Laws regarding Mischlinge (mixed-ancestry Jews) and treating most of them as fully Jewish.
This makes the canard that Hitler seized power legally somewhat meaningless in that his actions and those of his compatriots showed they never really wanted to be bounded by existing laws. They were operating on a different wavelength with regards to legality, and they took advantage of the lax enforcement of the existing laws after the Depression hit to maximize the efficacy of the SA. This antidemocratic ethos was not just limited the the NSDAP and many of their enablers inside the various state agencies perceived they could instrumentalize Hitler and his ilk for their own ends. This illustrates the fundamental danger of letting in explicitly antidemocratic groups and ideologies into the democratic process as they can cause a significant amount of damage to the body politic as a whole.
Sources
Evans, Richard J. The Coming of the Third Reich. New York: Penguin Press, 2004.
Johnson, Eric A. Nazi Terror: The Gestapo, Jews, and Ordinary Germans. New York, N.Y.: Basic Books, 1999.
Swett, Pamela E. Neighbors and Enemies: The Culture of Radicalism in Berlin, 1929-1933. New York: Cambridge University Press, 2004.
Wachsmann, Nikolaus. KL: A History of the Nazi Concentration Camps. New York : Farrar, Straus and Giroux, 2015.