They use multiple OCR engines. Some developed in-house and some proprietary ones. A blog post mentions I.R.I.S. as one of the proprietary ones.

They don't offer OCR publicly, instead, they generate a list of possible candidates to match against search queries (fuzzy matching).

From one of the blog posts: "Employing multiple reco engines is important not only because they specialize on different types of text and languages, but also as this allows to implement ‘voting’ mechanism — analyzing word alternatives created by diverse engines for the same word allows for better suppression of false recognitions and giving more confidence to consensus variants."

More: http://blog.evernote.com/tech/2013/07/18/how-evernotes-image...

http://blog.evernote.com/tech/2011/11/01/even-grittier-detai...

http://blog.evernote.com/tech/2011/09/30/evernote-indexing-s...

If I recall, they don't do traditional OCR, rather they build a term probability database that lets them do matching on search terms. Both Evernote and ABBYY seem to have ties to a specific Russian research group.