These are how I would understand the words in British English. American English may use slightly different meanings, or have the words be applicable in other situations.
A grade is the overall score in education. If you got 9 points out of 10, your grade might be an
A, or it could be a number like in Germany's Abitur grading. Scotland uses both letters and numbers in grading (A1, A2, B3, B4, C5, ...).
There is some overlap between a "mark" and a "grade." A mark could refer to a point, as in:
This question is worth 5 marks.
How many marks did you get?
I got 47 marks.
Or it could refer to your overall score, as in:
What mark did you get?
I got an A+ or I got 47 out of 50.
If you were referring to a test that had been graded, you could also say that it has been "marked."
A point is more general, and could apply to education, sport, computer/board games, and so on. In the UK, for example, UCAS points are used to weight different qualifications, and in Scotland SCQF credit points are based on hours of study. In tennis, points go 0 ("love"), 15, 30, 40, "game." In football, each goal is a single point.
A score is also more general, and is usually to do with the total number of points accumulated in a single game, match, or sitting. Like a point, a score can apply to education, but can also be for sport (the 2014 World Cup final's score was 1–0, one–nil; Germany scored one point/goal and Argentina scored none), computer/board games, and a number of other things.
An everyday example is that banks and other lenders use a credit score to show how risky it is to give someone a loan.
To actually answer your question (i.e. "which of these make sense/are/natural?"):
I got a very low mark in the midterm test.
I got a very low grade in the midterm test.
I got a very low score in the midterm test.
These are all fine, because each of the words can refer to your overall result in the test. For the first sentence, you could also say that you "got low marks" in a test.
I got a very low point in the midterm test.
Although it would be understood, this isn't correct. A point is a unit of score (like a centimetre is a unit of distance, or km/h a unit of speed). You can't have a "low kilometres-per-hour," but you can have a "low speed."
You could say that you "scored few points" or "scored a low number of points" in a test.
I want to read out the test marks to you.
I want to read out the test grades to you.
I want to read out the test scores to you.
Again, these are correct because they refer to your overall result in the test. It would be more natural for me to say "I want to read you the test scores" or "I want to read out the grades," but that could just be a difference of dialect.
Specifically, these sentences mean that multiple grades or scores will be read out. For example, the scores of multiple people or on multiple tests.
Saying "test grades" does sound slightly redundant to me, since a "grade" will almost always be for a test.
I want to read out the test points to you.
Like in example one, this would be understood but doesn't sound natural to me in this context. Using the speed example as above, you wouldn't "read out the kilometres-per-hour," you would "read out the speed."
Question from comments
can we say: "What (grade / score) did you get?" too?
Using "grade" here would be fine. You could also say:
What was your grade on that test?
Asking "what score" sounds a little unnatural to me (although I can't say precisely why), and I would instead use:
How did you score on that test?
What was your score on that test?
You could also avoid using the "score" altogether, as in:
How did you do on that test?