Correct usage of modal verbs: should have / might have / would have

These are arranged in approximate order of certainty from most to least, but it isn’t quite linear like that because these have different nuances:

1. The second lecturer said that the first lecturer will have taught this section in his own classes.
2. The second lecturer said that the first lecturer must have taught this section in his own classes.
3. The second lecturer said that the first lecturer would have taught this section in his own classes.
4. The second lecturer said that the first lecturer may have taught this section in his own classes.
5. The second lecturer said that the first lecturer might have taught this section in his own classes.
6. The second lecturer said that the first lecturer could have taught this section in his own classes.
7. The second lecturer said that the first lecturer ought to have taught this section in his own classes.
8. The second lecturer said that the first lecturer should have taught this section in his own classes.

Perhaps there’s even a case to be made for shall have taught, but that is a different thing entirely, more like a command.

By "the second lecturer is taking classes nowadays." I assume he is teaching the class or is he still a student taking or attending the classes. Some places use taking to mean either one.

In either case perfectly fine sentences can be made of each of the verbs you listed. The most boring one might be what they had in mind as the most certain to have happened; They must have taught this section. After Must they might line up in likeliness as: Would have; Should have; Might have. Without some other context suggesting a follow up it is mere speculation.

Should have can actually be used if the subject was actually covered. As in:"I'm glad he covered the topic; he certainly should have! There is no contradiction just affirmation.