Austria was for the longest part of its history considered an integral part of "Germany". Every Emperor from 1438 onwards to the very end of the Holy Roman Empire (with one short exception) was a Habsburg (i.e. from the Austria's ruling dynasty), Vienna was Germany's largest city by far throughout most of the Early Modern Era etc. About from 1740 onward, i.e. when Friedrich II ascended to the Prussian throne, a sort of "Cold War" began within the German territories with Protestant Prussia to the north and Catholic Austria to the south. It wasn't really that cold a war, either, with the two coming to blows several times throughout Friedrich's reign. When the Holy Roman Empire was dissolved in 1806, and after the Napoleonic Wars had come to an end, the 41 remaining German territories came together to form the "German Federation" of which Austria naturally was also a member - conversely, it didn't join the German Customs Union started in 1834, however, because Austria's chancellor Metternich was against the idea of such a union. The National Assembly that came together after the 1848 Revolution actually tried to reinstitute a unified German Empire, but when it offered the crown to the Prussian King, he downright refused it - both because this would definitely have led to Austria's permanent exclusion from this new German nation for a number of legal reasons and because Austria probably wouldn't have accepted a Prussian Emperor, and also because the Prussian King was disgusted by the idea of being made Emperor by an act of parliament instead of being crowned "by the grace of God". Roughly two decades later the situation was very different, however. Even though the 1848 Revolution had largely ended in failure, many of its ideas and especially the growing nationalist sentiment endured until (and I am really oversimplifying here) the new Prussian prime minister Otto von Bismarck realised that if a unified Germany really was coming sooner or later, then he wanted to put Prussia on top of it. Through a bold series of political manoeuvres, Bismarck managed to further stoke nationalist fervour at the expense of Austria. In 1866, Prussia went to war against Austria and the rest of the German Federation and won; the Federation ended and Austria left "Project Germany" for good. With the Franco-German War of 1870/71, the remaining southern German states also joined up the Prussian unification project and thus became part of the new German Empire. Austrians continued to identify and be identified as ethnically and culturally German, however. This only really changed with WW2, but even to this day you won't have to look long until you find people in Germany or Austria who still believe that the two countries should be one. Naturally, virtually all of those are to to far right.
Switzerland is, of course, a hodgepodge of various languages and cultures with only a part of it being "German". From the Middle Ages onwards, a loose confederation of cities and other territories started to agitate against the overbearing influence of various noble houses, mostly against the Habsburgs who originally hailed from the area. There followed various conflicts, federations, treaties and so on - it's really complex and also still strongly coloured by nationalist Swiss historiography, so I'll spare you the details (and me the effort of properly looking them up) and just say that from the Late Middle Ages onwards, the "Alte Eidgenossenschaft" de facto formed an independent block within the Holy Roman Empire, and in 1648 it left the Empire for good. Due to this early separation from a larger "German" framework and because of the legacy of a struggle for independence (or rather: the mystification and glorification of early Swiss history into such a struggle) as well as the multi-cultural structure of Switzerland, pan-German nationalist sentiment never really found much of a place in Swiss society. This is also why standard German never became the normal register of speech in Switzerland, as the local dialects were specifically fostered and supported by the authorities and the elites as a sign of a separate Swiss identity.
Liechtenstein was a part of the Holy Roman Empire and then the German Federation until the very end - some even declare it to be the only principality of the HRE that is still extant. Liechtenstein always was closely tied to Austria to such an extent that its monarchs resided in faraway Vienna until 1938 (!) that it followed its neighbour's political trajectory away from a unified German nation as well. Prince Franz Josef II (reg. 1938-1989) was very hostile towards National Socialism - his move from Vienna to Vaduz was strongly motivated by the incorporation of Austria into the Third Reich shortly before he took the throne. While there was a National Socialist and pan-German "völkisch" movement in Liechtenstein, the prince's hostile stance and the cooperation of all other major parties with the common goal to minimise Nazi influence in the country led to the movement never really taking off. (As an aside: Hilti, one of the world's largest tool manufacturers, was established by a fanatical Liechtenstein Nazi who even went so far as to voluntariliy join up with the Waffen-SS in 1941).
Finally, Luxemburg used to be an important duchy during the Middle Ages, but after its namesake dynasty died out in 1437, it got sold to Burgundy and later became a Habsburg territory. For the following centuries, the area repeatedly became the scene of conflicts and open warfare between the Habsburgs to the east and the French Valois and Bourbon to the west. In 1815, the area finally got declared to be a sovereign grand duchy (although a lot of what used to be "Luxemburg" in historical memory got ceded to France and later Belgium); however, its monarch was the King of the Netherlands, who naturally resided elsewhere. Luxemburg was a member of the German Federation as well as the Customs Union, and the city of Luxemburg was a German "federal fortress" (Bundesfestung) which was mostly garrisoned by Prussian troops. During the late 1860s, Bismarck tried to secure French non-intervention into the German unification process by trying to sell them Luxemburg. The Dutch King William III was completely broke and initially agreed to the deal, but backed out of it again when it became public and faced heavy criticism. While many citizens of Luxemburg indeed identified as "German", other were sympathetic towards France, where many of barely industralised Luxemburg's populace had found employment. This "Luxemburg Crisis" ended with an international treaty securing the status quo and enshrining complete neutrality of the duchy akin to Switzerland, which also eliminated any remaining possibility of the country joining the German Empire shortly afterwards. The country only became truly sovereign when in the Netherlands Queen Wilhelmina took the throne in 1890; Luxemburg law didn't allow for a female monarch, which meant the separation of the duchy from the Netherlands. The Germans invaded in both World Wars, which didn't do much to endear the population to any pan-German ideas. In fact, Luxemburg saw significant resistance to German occupation during WW2. As part of this establishment of a specific Luxemburgian identity, the German dialect spoken in Luxemburg saw a lot of official support to the point that it got declared a language of its own and was elevated to one of the three official languages of the state in 1984.