Yoda speaks with difficulty with people, so what is his real language?
Does exist a language for same species creatures of Yoda? (es. Shyriiwook for the Wookiees)
TLDR:
Language: Variation on the Galactic Basic Standard**, which he speaks fluently, but in an unusual manner which may make it sound like he has difficulty. It is not a dedicated language just for his species.
Answer:
Yoda's language appears to be a form of The Galactic Basic Standard. Wookiepedia describes it as:
...an unusual form of Basic utilized by Jedi Grand Master Yoda and others of his tridactyl species, including Yaddle; it was characterized by an object-subject-verb format. However, another member of this species, Vandar Tokare, did not use this dialect.
So it appears most if not quite all of his species spoke this language, in this way (an Object-Subject-Verb order). Given this, his species do not have a dedicated language, such as Shyriiwook for Wookies.
As to why he speaks this way, I believe that is a little harder to understand. I don't believe any Star Wars canon ever really addressed this (in fact, Yoda's entire species has been kept under wraps in most of the Star Wars canon released - they don't even appeat to have a name).
In Fate of the Jedi: Backlash, Ben Skywalker suggests:
"After nine hundred years, [Yoda] was sick of hearing the same old things the same old way. Use the same old cliché phrases too long and people stop hearing their message."
Of course, this is hardly definitive. Perhaps it was a decision made to make him sound like a wise old master, or to deliberately stand him apart from those around him, as a focal "oddity".
So the "what" appears to be Galactic Basic Standard. The "why" is unknown.
On a final, Star Wars movie related note, his manner of speaking is never referenced or commented on in the films or series, as far as I'm aware.
Edit:
As always, our colleagues at the Sci Fi Stack have discussed this, if anyone wants another list of answers to peruse.