I think that the best way to approach the type of learner you refer to is to teach through speaking and listening.
It is not your role as an EFL teacher to teach literacy skills. Furthermore, teaching literacy skills is a specialised job and I don’t recommend you attempt it.
I suggest you use speaking, repetition, drills, recordings as much as possible. During presentation of language, use visual aids to help get the meaning across. At beginner level, it’s probably best if they listen to your voice during presentations; as they progress, you’ll be able to use recordings. When you present vocabulary, use pictures, mime and realia. To present grammar structures, create situations by using pictures, mime, etc and language the students already know. If you speak their language, you can use that too. I think there are situations where using the students’ native tongue is justified and this is definitely one of them. You could also ask for a teacher’s assistant during presentation – could a member of staff help? Perhaps a member of admin staff?
After language has been presented, do lots of controlled practice using drills and repetition. You could take a look at Jazz Chants by Carolyn Graham. This book has lots of chants for students to repeat in chorus; they repeat basic language in a fun way. Songs can also be good for repetition; take a look at Beginner level English File by Oxford University Press.
The same goes for free practice, you will need to give as much oral practice as possible. You can take a look at books for speaking practice and use the activities or adapt them.
I have answered your question as if your students really are illiterate, but that is quite rare. Are they able to write, copy or read single words? If so, you can have students copy vocabulary and short phrases. The meanings can be illustrated through pictures that you provide or that students draw themselves.