You can not buy any units other than Hungarian.
Well it is supposed to be a Hungarian campaign after all...
Sorry, but I do not really like the idea of having units with different nationality in the Hungarian Army core. This is of course not because of some kind of nationalistic feelings, but mainly because of gameplay issues. If the player would get access for German units in any scenario he would simply start big time shopping and forget about the weaker Hungarian units. Naturally, this would unballance the campaign.
This option was made possible for the Africa Korps official add-on, where the situation is the opposite: in the German campaign the player has the option to purchase the generally weaker Italian units, if he wants some more flavour/historical accurarcy/challange. Apparently, in bebro's recently released Japanese campaign the player cannot even purchase Imperial Japanese Navy or Marines units (IJN), only that of the Imperial Japanese Army. This is a severe restriction, which makes the campaign more challanging and intersting and also the occasionaly added no-purchase bonus Japanese Navy core units (marines, Zero fighter, etc) more prestigious.
The other reason is pure historical: especially in the first half of the war, as opposed to the Western Allies, Germany was reluctant to give its latest weapons to its allies, fearing they would change sides, as it evetually happened with most of them. For instance, early in the war, Hungary asked the manufacturing licence of the PzIV tank from the Germans, who refused to do so, instead, they offered the already obsolete PzII, which, in turn was refused by the Hungarians. In 1943, Hungary asked for the plans of the Panther tank, only to get an offer for the PzIV finally, but, by that time this tank was also reaching the end of its life cycle, so Hungary decided to carry on with its own Turan tank family.
As for the other minor Axis countries, such as Romania or Slovakia, well, throughout most of the war Hungary was in a "cold war" with most of these because of territorial disputes, so having them in the Hungarian core would be a bit strange, too. Not to mention that, in case of Romania, the cold war later "melted" to a full scale war (SPOILER!).
However, later I may examine the possibility of adding more aux slots and allow the player to purchase aux units of other countries in certain scenarios. But the budget will remain tight so it might be a waste of prestige.