Hi Nataly,
while I haven't encountered such problems in any of my classes I can understand the difficulties you are facing in teaching a complex language like English to students with non Germanic language backgrounds and learning disabilities such as dyslexia. Since I am no expert though I looked around online and found several books and articles which share strategies and personal stories, I hope these help!

http://findarticles.com/p/articles/mi_qa3809/is_200001/ai_n8882589/

http://www.ldonline.org/article/Learning_Disabilities_and_Foreign_Language_Learning

http://www.thefreelibrary.com/Dyslexia+and+foreign+language+learning-a0146219121

http://www.amazon.com/Dyslexia-Foreign-Language-Learning-Margare/dp/1853469661

The central difficulty for dyslexic students is poor phonemic awareness.  Phonemic awareness is the ability to appreciate that spoken language is made up of sound segments (phonemes).  In other words, a dyslexic student’s brain has trouble breaking a word down into its individual sounds and manipulating these sounds.  For example, in a word with three sounds, a dyslexic might only perceive one or two.
Most researchers and teachers agree that developing phonemic awareness is the first step in learning to read.  It cannot be skipped.  When children begin to learn to read, they first must come to recognize that the word on the page has the same sound structure as the spoken word it represents.  However, because dyslexics have difficulty recognizing the internal sound structure of the spoken word to begin with, it is very difficult for them to convert the letters of the alphabet into a phonetic code (decoding).
When a child has a learning difference, they need a very specialized reading or tutoring program.  Children with learning disabilities are usually unable to follow the school’s curriculum.  They cannot learn using standardized worksheets and workbooks.  

To teach a child with a learning difference how to read, the teacher must begin with the recognition of the letters, the sounds of the letters, and the sounds of letter combinations (phonemes).   This teacher needs to be a specialized and trained teacher in Orton-Gillingham  - or any other program used for students with learning differences.  It must be an extremely structured program that is systematic and cumulative.  This means that, like a pyramid, the base or foundation must first be strong enough to support the entire structure.  With a solid and strong foundation students will be able to recognize words through decoding.  Usually after a student has mastered the decoding process, the fluency and comprehension will follow.  

A specialized and well -trained teacher or tutor of students with learning disabilities will also enhance executive functioning skills, which are often quite weak in students with dyslexia, auditory and visual processing disorder and ADHD.  These students also will need to learn one-on-one with very few distractions in a multisensory, structured learning environment.

I'm assuming you teach Russian phonetically. Do you also teach English phonetically? I hope so. In this country, due to the nuttiness of our Education Establishment, we have so-called Reading Wars, where the common sense of phonics is constantly battling against the flawed ideas of Whole Word. A lot of this stuff is preached as if it's religious truth, and may have contaminated Mother Russia. See article for brief intro to the issues, the chief of which is the question of whether there are any dyslexics?

(Also note my site Improve-Education.org, which has 6 articles about reading, several about teaching efficiently, one about Pavlov, and in general many intellectual but clearly written articles you could use in diverse settings.)