Could might have been

As they stand, only the former seems correct. It suggests that it was possible to use certain Danish words in the plural at that time. In direct speech, "might be" is limited to the present/future.

Thank you. Are you a native English speaker? If yes, do you think COULD doesn't convey the meaning as clearly as MIGHT?

-At that time some words might be used in the plural. (=you had a choice, singular or plural)
-At that time some words might/may have been used in the plural. (=I don't know whether at that time

OttoJOne hundred years ago, in the Danish language, many words could be used in the plural.

This suggests that this was permitted, though it doesn't fit the situation particularly well.

OttoJOne hundred years ago, in the Danish language, many words might be used in the plural.

This suggests that on a whim one might decide to

OttoJAt that time some words might be used in the plural. (=you had a choice, singular or plural)

This is possible with the meaning you've specified parenthetically.

OttoJAt that time some words might/may have been used in the plural. (=I don't know whether at that time those words could be used in the plural.)

This is also