Ok, so a bit late to answer your question but here it goes:

The Heimwehr is an odd political animal, part para-military organization, part political movement that had ties both to the Christian-Social camp and the Deutschnational (German national, the people propagating a racialist-motivated union between Austrian and Germany) camp in Austria.

The Heimwehr or rather the Heimweheren (in the beginning there was no central organization) were founded from 1920 and are comparable with the German Free Korps, i.e. as para-military formations with a racialist right-wing agenda and the purpose of fighting against the border changes following the loss in WWI as well as fighting against the left and the democratic revolution. It is no big surprise that the man who had ordered the murder of Karl Liebknecht and Rosa Luxembrug, Waldemar Papst, went to Innsbruck after the Kapp Putsch in which he was involved failed in order to help build the Heimwehr in the Tyrol.

Similarly, in Carinthia and Styria, the Heimwehr formed in order to fight Yugoslav troops in the southern regions of Austria. These Heimwehr units had very strong ties to the Free Korps in Germany as well as to the White troops in Hungary fighting the Soviet Republic of Bela Kuhn.

Basically, in the beginning the Heimwehr or rather the multiple Heimwehren were para-military units whose political agenda was xenophobia, anti-democracy, and anti-Bolshevism.

Post 1927, this changed somewhat. On January 30, 1927 members of the local Heimwehr militia had fired shots on a Social Democratic meeting in the town of Schattendorf in the Austrian state of Burgenland, killing a small child and a war veteran. The members of the Heimwehr in Schattendorf were indicted for murder and subsequently acquitted later that year. This acquittal lead to massive protests of Social Democrats who – rightly – felt that this was a massive miscarriage of justice. During a demonstration in Vienna, the Justice Palace was set on fire and protests spread far and wide in Austria. Heimwehr units were used to violently suppress these protests.

The so-called Schattendorf incident had far reaching consequences. Within the Heimwehr units, it lead to a renewed sense that there was the danger of socialist revolution from the left. Thus the Heimwehr organized into a new centralized structure also aiming to become more than merely a fighting tool for the non-socialist parties against the left.

It also lead to the Heimwehr adopting a new political creed that can be best characterized as Austro-Fascist. Austro-Fascism is hard to tie down for someone not familiar with the Austrian political landscape but it can best be described as a peculiar mix of Mussolini Fascism, Nazism, and Catholicism. In 1930 the Heimwehr elected Ernst Rüdiger Starhemberg as their new leader and swore the so-called Korneuburger Pledge. They aimed at establishing a Catholic and Fascist inspired corporative state with a particular influence of Nazi-esque racialism.

The Corporative state is a concept that rejects a capitalist as well as communist model of social organization and that ostensibly aims to establish a model of society organized along corporate lines, meaning that – with a nice tinge of pseudo-feudalism – your social status and influence on social affairs depended on your corporation in the sense of the historical estate, i.e. farmers, nobles, priests, work men etc. The racialism of the Heimwehr found its outlet in such provisions as excluding Jews and other "subhumans" because of their association with communism or the general argument that they were "foreign" to the Austrian Volk.

One thing the Heimwehr was split on however was the issue of unification with Germany. While the original Heimwehren of the early 20s had almost all been in favor of unification out of racilaist arguments. This however changed during the 1920s and especially after the establishing of the Austro-Fascist regime in 1933 and the Austrian civil war of 1934. With its decidedly strong Christian-Social influence, the Dollfuß / Schuschnigg regime pushed Austrian nationalism against the unification with Germany because of their strong Catholicism infused ideology that was massively at odds with the völkisch line of the Nazism that the Catholic Church as an institution was international and therefore an enemy to the Volk.

This split the Heimwehr into several factions, with some switching over to the – at the time – illegal Nazis in Austria while others remained an pushed for a more Nazi friendly line within the Heimwehr itself.

So, on the whole, the political aims and ideology of the Heimwehr were a rather peculiar ideological concoction that grew out of the specific Austrian context and is best summed up under the moniker Austro-Fascism.