I can't speak for Lithuania but Austria and Prussia were just not allowed to be kingdoms.

The Holy Roman Empire always had a thing against kingdoms and in fact while it existed the only kingdom in it was the Kingdom of Bohemia and that was mostly because of established tradition. Generally kingdoms tend to be independent and by definition none of the countries in the Holy Roman Empire were since they were all subjects to the Emperor.

The thing with the Archduchy goes back to the Golden Bull of 1356, issued by HRE Charles IV. of Bohemia (of the House of Luxembourg), which took the established practices and agreements of the electors and election process and made them into law. This included the identities of the seven electors whose responsibility it was to chose and crown the Emperor but also gave them certain privileges like the right to mint their own coinage and immunity from the Imperial Supreme Court.

Austria, which at that time had already gotten a good diplomatic foothold, was now pretty miffed that they had been shamelessly ignored in that document. So two years later Rudolf IV. of Austria invited a few shady guys to forge him something that would give him access to the same privileges. They then went and drew up a nice document and gave it the proper Imperial look by taking the seal off of the Privilegium Minus, an official Imperial document issued in 1156 by Emperor Frederick I Barbarossa that elevated the margravate of Austria to a duchy in recognition of their help against Bavaria, which is why this forgery is now generally known as the Privilegium Maius (and why we only have copies of the original Privilegium Minus - lousy destructive forgers!).
The title of Archduchy was mainly chosen because no sane Emperor would grant the title of king to anyone and thus make him an almost equal.

Unfortunately, the Emperor was not as convinced as Rudolf had hoped and as such never sanctified it. Maybe it had something to do with the zealous forgers including signatures from Julius Caesar and Nero to make it seem "more historically established", maybe Charles just didn't like Rudolf... anyway, in 1440 another Habsburg managed to get himself elected as Emperor Frederick III., and since it was in his family's best interest he could then just confirm the claims of the Privilegium Maius himself, which he did in 1453.

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Prussia on the other hand was inherited by the Brandenburgian branch of the Hohenzollers, but only the Eastern part of Ostpreußen while Westpreußen with Danzig belonged to Poland. The king of Poland also called himself King of Prussia, which is why his belongings there were also known as Royal Prussia while the Hohenzoller lands were Ducal Prussia since they were subordinates of the King of Poland in their roles of Dukes of Prussia (but at the same time also subordinate to the Holy Roman Emperor as Dukes of Brandenburg).

And even when they managed to get all of Prussia under their control they had to get the Holy Roman Emperor's approval since they were after all still his subject. And as mentioned above no sane Emperor was going to allow one of his subjects to claim the title and prestige of a king, which is why for some time after the Hohenzollers were known as King in Prussia (not of as you'd expect) to signify that while they were sovereigns outside they were still merely subjects in the Holy Roman Empire. Though that distinction faded over time.

Sources:
Lhotsky, Alfons: Privilegium maius. Die Geschichte einer Urkunde
Weinrich, Lorenz: Quellen zur Verfassungsgeschichte des Römisch-Deutschen Reiches im Spätmittelalter (1250–1500)