OK so this has confused many people I know but it is, in essence, rather simple. The most simple answer is that they were extremely right wing, however, confusion comes from the fact that Hitler was said to support many things typically concerned with leftist politics.

Let's start with the name, the NSDAP- or national German socialist workers party. In the early 1920s, Germany was trying to adapt to the new democratical political system which was put in place after the signing of the Treaty of Versailles in 1919. This system allowed universal suffrage and through proportional representation, every German could be represented in the Reichstag. However, this is considered by many historians to have been the most democratic system in the world at that point in time, which sounds good, however, Germany - coming from a long history of monarchical ruling - simply wasn't ready for it. Elections were frequent and there were simply too many parties, many claiming to want the same thing for the people. No one party could gain a political edge and so the Reichstag consisted of many squabbling parties who were slow to act which angered many who were used to the swift ruling of the Kaiser. One of the fledgling parties which tried to gain an edge was the NSADP.

Earlier I highlighted the "socialist worker" section of the party name and I did this because it was done in an attempt to try and gain the working class vote, by claiming to represent them, the Nazis hoped to gain some extra votes.

Hitler believed democracy was weak (and many supported him because of the disastrous early years of the Weimar) and that one strong ruler should make decisions on behalf of the people. He cited his time in the military during the great war as the greatest of his life. However, he also believed that the German farmers (the mittelstand) and artisans were the backbone of Germany and many of his "socialist" policies were aimed at them. He promised autarkey (essentially the idea that germwny would bevome self sustaining) to farmers ensuring that, under his rule, German farmers would prosper as the state would buy from German farmers before importing goods (this was really an attempt to prevent hunger in any future wars as happened during the naval blockade of ww1) and, in fact the rural communities (which made up around 20% Germans) became the core support group for the Nazis as they had been hit by the great depression worse and earlier than most (the stock market crashed in October 1929 yet many farmers and small traders were economically hit in late 1927/early 1928) and so, in what is known as "the farmers revenge" they voted for the NSDAP. Others considered his idea of a Volksgemeimshachft to be a left wing idea. This was essentially a "people's community" were every German worked for the good of Germany and reaped the benefits of their labour. This meant that, in essence, a worker and a junker (wealthy industrialist) would be cinsidered equal. Then you can consider the strength through joy programme in which the state provided day trips, cinema tickets (to see what was largely propaganda) and other similar excursions which were supposed to reward the people. Hitler remarked during a speech in Kiel:

The NSDAP is an organisation which does not recognise proletarians, does not recognise bourgeois, farmers, manual workers and so on; instead it is an organisation based in all regions of Germany, composed of all social groups. If you ask one of us 'young man, what are you? Bourgeois? Proletarian?' He will smile 'I am German! I fight in my brown shirt' that is indicative of our significance, we do not aspire to be anything else, we are all fighting for the future of a people? We are all equal in our ranks"

The idea of all men being equal, all being of equal footing regardless of class is considered by many to be a typically left wing idea and from that, strength through joy, autarkey and other similar policies and the party's name, it is clear to see why many consider the Nazis to be left wing.

In truth, however, it was extremely right wing, Hitler, as I mentioned previously, loved the military, he believed all German boys should grow to be strong soldiers (and all girls to be wives and mothers), war is strongly opposed by those on the extreme left who believe that soldiers are often pawns who have more in common with the men they are trying to kill than the men who are telling them to shoot. The party believed in Lebensraum (living space) for the German nation which would be granted by invading and forcefully taking lands from neighbouring countries. Hitler held right wing views concerning gender, men should be strong and fit, if they weren't then they didn't deserve a place in Germany, girls should be seen but not heard, they should cook and clean and care for their family and if they couldn't (or didn't) then they didn't deserve a place in Germany.

However, much of what Hitler promised to the people which was seen as left wing did not work, autarkey led to many farmers being unable to produce the amount of food that was required of them and they were paid small amount for what they did receive while farms, under law, became attached to a family, no one could buy someone else's farm and it was to be passed to the children of the current owners which left many farmers stuck with old equipment as they couldn't afford new machines such as tractors as no bank would loan to them as they had no collateral.

Hitler held the belief that those of minority races, the disabled - physically or mentally -, homosexuals, communists, Jews and other groups were not truly human, they were parasites who didn't deserve to be German. His beliefs in relation to eugenics was that all of this was the result of poor genes and could be bred out.

The Nazis, when they reached power introduced many policies which were extremely right wing but the ones I mentioned above were seen, on the surface by some, to be left wing and along with the name, many saw it as a left wing group, however, there were considerably more right wing policies under the Nazis than the poorly constructed left ones and indeed, many workers who generally supported the left continued to do so (even after Hitler took power even if they weren't always vocal about it) and only a very small percentage of the workers actually voted for the Nazis suggesting that they could see through the facade of supporting the working class.

Tl;Dr the Nazis were a right wing party with militant ideals, however, due to their party and name and certain policies some considered/consider them to be left wing.

Not to discourage any new answers coming in, but I think you will find this answer by /u/G0dwinsLawyer helpful and interesting.