This is just my feeling as a native Japanese speaker.
They are interchangeable in most cases but have different implicit nuances.
Some articles just say "interchangeable" because the differences are really tiny, especially verbal communication. For beginners or intermediate-level learners, it doesn't matter, because the nuances are less than the pronunciation effect, so until your pronunciation becomes perfect as native, they are interchangeable.
On the other hand, when it is used in text like a novel, lyrics, dialogue, etc... the author has the reason why choose one.
And your feeling is correct. "のか" has some more pressure than just "か".
But this is not always correct. In this sentence "君が何したのかしりたい", it is used "君" and "が" and "何した". They are also some alternative like "あなた", "お前" or "(name)", and "は", and "何をした".
For example, those sentences are also translated "I want to know what you did"
- 君 が何をしたのかしりたい
- お前 が何をした かしりたい
but the nuances or images are different.
So those words already show some relationship between "you" and "I" and some situation.
- "君" means "I" are higher position than "you" or really closer with "you".
- "何したか" have impatience feeling than "何をしたか".
- "が" feels like not one of them but you(Obj) than "は".
In brief, the sentence feels like "I" doubt something about "you" already. So in this situation, "のか" make the sentence some more interrogative because the "のか" emphasize the feeling.
In my opinion, "のか" can emphasize the sentence's feelings than just "か".
So If the sentence just has flat nuance, they are interchangeable.
For example, (I want to know who did fix the problem.)
- 誰がその問題を解決した かしりたい
They are the same feeling,
- 君がその問題を解決したのかしりたい (I doubt you but...)
- 君がその問題を解決した かしりたい (I just want to know if you did)
They are not the same for me.
I hope it helps you!