What is the meaning of "өгүүлрүүн"?
I saw a sentence.
Тэр өгүүлрүүн:
-Хүн гуай... надад хонь зураад аль!
I guess өгүүлрүүн is related with өгүүлэх.
What is the difference between өгүүллээ and өгүүлрүүн?
There is no difference between "өгүүллээ" and "өгүүлрүүн". However, "өгүүлрүүн" is not used in spoken language anymore - it's quite archaic. I think you can find this word in fairy tales, very old books or books about ancient times.