Most of the acronyms I know are pronounced phonetically as they are in both your example and most of the time in English. However just as English turns some acronyms into their own words, the same happens in Japanese. I can't think of a specifically defined rule and to further muddy the waters, some of these are influenced by some of the people or companies representing them.

Your two examples would most likely (some people would prefer the proper Japanese words - such as the second example) be used instead.

AXQ [AXQ] エイエクスキュー / Ei-eks-kyu {Unsure of specific example that you are referring to} JSOC [統合特殊作戦コマンド] ジェイソック / Jei-sok

More Examples...

• Acronym [日本語]
  • カタカナハツオン / English pronunciation

• NASA [米航空宇宙局]
  • ナサ / Nae-sa
• JAXA (Japan Aerospace Exploration Agency) [立行政法人宇宙航空研究開発機構]
  • ジャクサー / Ja-ksa
• NISA (Nippon Individual Savings Account) [日本少額投資非課税制度]
  • ニーサ / Ni-sa
• MOFA (Ministry of Foreign Affairs) [外務省]
  • 外務省 / Mo-fa
  • ※ Only usually referred to in Japanese as 外務省

ES, DE, EN are all ISO codes -- "ISO" as in "International Standards Organization" (technically, it's the "International Organization for Standardization"). These codes are used worldwide, particularly in programming and other technical contexts. In localization engineering, I've dealt with these codes for years. There's no particular value in developing a competing standard—the point of a standard is that, well, it's the standard.

That said, Japanese already has a convention for abbreviating country names in text -- usually the first kanji of the country's full name.

• 英【えい】 for the UK / English, from 英【い】吉【ぎ】利【り】[　]{す} (Igirisu, probably from Portuguese Inglês, with the spelling from Chinese)
• 露【ろ】 for Russia / Russian, from 露【ろ】西【し】亜【あ】 (Roshia, from Russian Росси́я (Rossíja), with the spelling probably partly from Chinese)
• 仏【ふ】 for France / French, from 仏【ふ】蘭【らん】西【す】 (Furansu, ultimately from French France, spelling derivation unknown)
• [独]{ど or どく} for Germany / German, from 独【ど】逸【いつ】 (Doitsu, from Dutch Duits //dœy̯ts//)
• 中【ちゅう】 for China / Chinese, from 中国【ちゅうごく】 (Chūgoku, from Chinese 中國)
• 日【にち】 for Japan / Japanese, from 日【に】本【ほん】 (Nihon)

And so on and so forth. Pretty much every country that has a kanji-based name can be abbreviated in this way. However, there are exceptions, so be sure to look things up:

• 蘭 for the Netherlands / Dutch, from 阿【お】​蘭【らん】​陀【だ】 (Oranda, from Portuguese Holanda with a silent "H", meaning "Holland" -- which historically was the leading province of the Dutch Republic and roughly corresponds to the provinces North Holland and South Holland, two of the twelve provinces that make up the present country of the Netherlands)

Update

As pointed out by Earthliŋ in the comments, sometimes Japan and Japanese are referred to by the abbreviation 和. This stretches back over a thousand years to the initial textual references to any country referred to as "Japan", when Chinese-language sources describe the country of "Wa" or 倭 (wa, literally "dwarf" in Chinese). See the 和 entry at Wiktionary for more detail. (Full disclosure: I edited that entry.)

One example of modern usage of this 和 to mean "Japanese" is this German-Japanese dictionary over on Amazon, using 独和【どくわ】 to refer to "German" and "Japanese". It's also the component used in the term 和文【わぶん】 "Japanese text", in contrast to 漢文【かんぶん】 or "Chinese text". Or in 和語【わご】 "Japanese language" in contrast to 漢語【かんご】 or "Chinese language".

Meanwhile, there is also a dictionary from the early 1600s that has been very important in discovering how Japanese sounds have changed over the centuries, called the 日葡辞書【にっぽじしょ】, using 日 to refer to "Japanese" instead.

So I think both 和 and 日 would work as one-character abbreviations for "Japanese". My subjective sense is that the two might be used in different contexts, but I do not understand the difference well enough to explain it here.

Please comment if the above does not address your question.