My Greek exegesis students see a lot of me this semester, thanks to exegesis of Luke being 4 credit hours. I set aside one hour just for Greek language revision, because despite a course in Greek grammar, they are not extremely capable masters of the Greek language.
I have been working on the challenge of expressing the four concepts of tense, mood, voice, aspect in Mongolian. There are several challenges.
1) Mongolian has no middle voice, so there is no easy correlative. This is a subset of the fact that Mongolian lacks a number of features that would easily correlate to Greek, especially it lacks an article, and it doesn't use relative clauses at all (it replaced them with adjectival or object clauses).
Anyway, I don't really believe there are true 'deponents' in Greek anyway, so I tend to treat all 'deponent' verbs as just another pseudo-conjugation. You don't meet that many middle voices (in the sense of distinct from passive), so I've kind of sidestepped that issue. Actually I work with a dichotomy of active/subject-reflexive
2) Mood is also a concept that is not easily correlated to Mongolian, since verbs do not undergo morphological change in subordinate clauses. The best I could find to correlate was 'conditional mood', but it is, more strictly, applied only to if- clauses. Indicative and Imperative are more easily explained. But the idea of 'mood' in general can be tricky.
3) Tense. Of course, tense is where you get the most overlap, except that current scholarly opinions about how temporal 'tense' really is in Greek is divided. My own short-hand approach is that epsilon prefix is a temporal marker, the perfect 'tense' is not perfect and not past, and that tense-forms outside the indicative generally only indicate aspect.
But of course my students are taught grammar with a traditional textbook, which means they have tense drummed into them. Generally I try and provide a on-the-fly Mongolian translation to make the sense of the tense clear. This usually works, except the perfect can be tricky.
This is probably the hardest. For a start, my students have not really been taught anything about aspect in general. Secondly, the idea is not clear within Mongolian grammar, so far as I can tell (and, coupled with this, I have a more technical understanding of Mongolian grammar than some of my students anyway). Thirdly, I haven't worked out how to translate 'aspect' in a strictly grammatical sense.
I suspect the way forward here is to start explaining what perfective and imperfective aspects 'look like', in terms of considering an action in a wholistic way versus a progressive sense. Then to talk about how, in the indicate, this is seen in the present, imperfect, and aorist. Then to give some terminology, and lastly to talk about the perfect tense. Learning to read the perfect tense as imperfective and presentinstead of perfective and past is somewhat counter-intuitive, but actually makes a great deal of sense of the Greek verbal system, and has some parallels with Mongolian tenses.