You can see this answer as supplementing MujjinGun's.
진리 is typically a generality, and 진실 a particularity.
Thus, truths in a learned body of discourse (physics, philosophy etc.) are 진리. But suppose you found out that noodles turn out better if you let the water boil first before you put the noodles in. You might say:
그것이 스파게티의 진리였다. (That was the truth about spaghetti.)
by which you put it forward as a general truth. (The Korean sentence sounds about as comical as the English one.)
진실 on the other hand concerns a particular thing such as (your example) Oswald's having killed or not killed Kennedy. But again it does not have to be a grand fact like the assassination of a president. It could be whether you took the dime from your mother's purse.
그렇게 사라진 동전에 대한 진실이 밝혀졌다. (So came out the truth about the missing coin.)
You will note that this distinction of generality vs. particularity tracks MujjinGun's finding out for yourself vs. having to be told.
In 진실 there can be a suggestion that someone might want to hide it. Thus,
진실을 알고 싶어요. (I want to know the truth.)
might be a way to urge someone to be truthful, in the sense of honest.
When there is no issue of honesty, you may use the word 사실, which corresponds to 'fact.' Thus, you may say
사실만 말씀하세요. (Say only the facts.)
if someone begins to speculate or give what is an opinion.
As for a higher level concept to subsume all three, perhaps 맞다 (to be true, right, correct or the case). So we get, e.g.:
물이 끓고 나서 면을 넣는 것이 맞다. (It is right to put the noodles in after the water has boiled.)
For a noun, we may consider 참 as opposed to 거짓. These are fairly abstract words meaning true and false, but 참 cannot replace any of the three words (진리, 진실 and 사실) in sentences like the above.
참말 is more or less the same sense as 진실. Thus:
참말이야? (Are you telling the truth?)
In 진리, there can also be a suggestion that the general truth was not easy to see. So 진리 is typically an object of 깨닫다 (realize) or 터득하다 (realize and acquire).
If there is no issue of difficulty (anymore), you may speak of 원칙 (principle) or 법칙 (law). For example:
만유인력의 법칙 (the law of universal gravitation).
This suggestion of difficulty or concealment is rather analogous to what you might find in 'true principles' and 'true facts,' which suggest that some false ones had to be got through first.
