There is some evidence to suggest that Yoda's speech is based on, well, English.
In this The Week article (I suggest reading the whole thing, the argument seems pretty convincing to me), Yoda's speech is compared to that which might be found in Shakespeare:
Round about the cauldron go; in the poison entrails throw.
Else the Puck a liar call.
For them the gracious Duncan have I murdered.
I like him not.
The article also offers some examples of what Yoda might sound like if his speech actually was based on other languages:
Is planet lost at Master Obi-Wan. (Gaelic)
I not you will-teach more today. (French)
I will my own counsel on them, who trained become, keep. (German)
As you can see, even using languages similar to English might come out too confusing for the average moviegoing audience. On the other hand, using archaic English associated with Shakespeare and the King James Bible is accessible enough to be understandable, while alien enough to set Yoda apart.
Not only that, but connecting Yoda to things like Shakespeare and the King James Bible goes a long way to make him seem more ancient and wise. In another answer on this site, I used this to explain why Darth Sidious talked the same way in Revenge of the Sith; Yoda's sentence structure reminds audiences (perhaps unconsciously) of school and church, which works to solidify Yoda's role as a religious teacher.
That said, it seems like another source of Yoda's unique speech is overenthusiasm. In the original trilogy, Yoda speaks normally almost as often as he doesn't:
"A Jedi uses the Force for knowledge and defense, never for attack."
"If you end your training now — if you choose the quick and easy path as Vader did — you will become an agent of evil"
"There is another Skywalker"
"That is why you fail"
However, it was the abnormalities of his speech that stood out more than the normality. Talking like Yoda turned into the equivalent of talking like a pirate or talking like Shakespeare: you take the things you know sound strange ('yarr matey', adding 'est' to the ends of verbs, etc), and use them as often as possible so everyone can tell what you're doing. Know, you will, when talking like Yoda I am, and the voice I don't even have to do. It seems like this explains most of the cringe-worthy later examples of Yoda's speech: it's based on Yoda's original speech, which is based on antiquated English that most people don't understand how to use.