A Google search on the search phrase

site:www.gutenberg.org "eggs is eggs"

turns up a decent number of uses, both British and U.S.... all quite old.

One is from William Thackeray. Another is from W. Somerset Maugham, "You've done it often enough before. Bennett. Don't expect any mercy from him, my lord. He'll do you in as sure as eggs is eggs." From Thomas Hughes' Tom Brown's School-Days, "I shall come out bottom of the form, as sure as eggs is eggs." From The Phoenix and the Carpet, by E. Nesbit, "had not taken the Lamb because he had a bad cough, which, cook repeatedly said, was whooping-cough as sure as eggs is eggs."

You'll love this one. This is from a U.S. source, attributed to "Edward Stratemeyer" (i.e. "the Stratemeyer syndicate," a group of writers that churned out adventure books for children--best known for the Tom Swift series). It's from Dave Porter in the South Seas:

At that moment Roger came in, looking thoroughly disgusted.

"Made me write half of it over again," he explained. "Oh, it's simply unbearable! Say, I am going to do something to get square, as sure as eggs is eggs."

"Eggs are eggs," corrected Polly Vane, sweetly.

Explanations of idioms are always suspect. That said, I've read that "eggs is eggs" is a distortion of the algebraic truth that "X is X," i.e. "X = X."

I have a very dim memory of this expression and so I think it has almost become archaic in the UK.  I am not sure about the USA but I wouldn't be surprised if it is completely unknown there.

There may be some other examples of idioms with non-standard grammar but idioms come to mind in specific situations so I can't think of any right now.  

Shakespeare and the King James bible have left us dozens of idioms, some of which may have otherwise archaic words and syntax.  Have a look here: http://www.phrases.org.uk/meanings/phrases-sayings-shakespeare.html

I saw: "all of a sudden" which is still said commonly but has non-standard syntax.