1. He scored 98 % in/on the English test.

2. He scored 98 points in/on the English exam.

(Which expression is correct? Do we have to use 'in' or 'on'?)

How you list the score depends on how the teacher scores it.

If there were 50 questions, and he got 40 correct, you would say ...

He got 40 out of 50 on the test.
or
He got 80% correct on the test.

If there were 100 questions, then either of the sentences you wrote would be correct -- but use "on" not "in."