Learn English – was working vs had been working

Either would be correct in this context.

Generally, the present perfect simple tense describes what has been happened so far, while the present perfect continuous suggests that something is ongoing or unfinished. The distinction isn't strong enough in this question to make a big difference.

Looking at two possible responses to the question might highlight the differences better.

(present perfect simple) I've worked here five years and I've loved every moment of it!

(present perfect continuous) I've been working here five years, but it's only recently that I was transferred to this office.

Similarly, one could say:

(present perfect simple) He's worked three hours today [he might work more, or he might go home after this].

(present perfect continuous) He's been working the whole morning [and he's still not done with his work].

I think that you'll be fine with any of the three in terms of clarity of meaning, though I'll discourage the past perfect in this case.

To my eye the issue seems more grounded in the first clause of the sentence: I usually have to read over, which establishes that the speaker engages in this behavior exclusively in the present (if not on a regular, ongoing basis). I think that present perfect and simple past are both appropriate here.

The relevance of the material that was taught is still in effect at the time of any given review, so the past perfect seems undesirable to me. It is also the case that the past perfect suggests that the pattern is not ongoing, which is at odds with the first clause's suggestion of an activity that still occurs. Such a reading would suggest that the speaker regularly reviews things taught in a specific period of the past, such as reviewing his/her own course notes from a specific class taken years ago, repeatedly. Conjugation in the second clause aside, I would not find this to be a natural reading of the sentence as constructed.

As for the other two options, with no context beyond what was presented in the OP I think that they are functionally interchangeable. Presumably each "unit" of teaching is what is being reviewed, whether that's by topic, course, day, semester, individual lecture or whatever. Each review is paired with some amount of teaching, but that the groupings are appropriate is implied by the larger sentence.

So, whatever unit is being considered, that material definitively was taught in the past-- presumably the speaker would not be reviewing planned material for an upcoming lesson at the same time as reviewing material actually delivered (if this is the intended meaning, the sentence itself does not suggest so). At the same time, it remains the case in the present that that material has been taught, and the review of that past action implies that that action is still relevant at the time of review.

TL;DR: My read of the sentence favors the simple past, as each "unit" of teaching is discrete and occurred only in the past with regard to any given review, and its relevance to the present exists only within the context of the review itself. The present perfect is also technically correct and appropriate but adds no useful information beyond what the simple past supplies. Past perfect may not be appropriate because it suggests a different meaning than the other two options suggest, leading me to believe that this is not the intended meaning.