Long solution (not sure if there's a more clever way without using a computer):

I will start with an assumption:

Since 21 is an odd number, question 20 is automatically false.

I will strikethrough false statements and bold true statements.

What we currently know:

1. Number 7 and 8 are false.
2. Four is false, twelve is true.
3. Number 20 is true.
4. One is true, two is false.
5. 3, 9, and 6, all are false.
6. I don't like strawberries.
7. Number 13 is true.
8. I like strawberries.
9. Number 5 is false.
10. Number 14 is true.
11. Number 11 is true, and 6 is, too.
12. 20 is false.
13. Number 1 and 8 are false.
14. Number 17 and 12 and 13 are false.
15. This statement is true, and so is statement 2.
16. The preceding statements are more true than false.
17. Either 11 or 15 is false, but 19 is definitely true.
18. Five and twelve are true.
19. There are more than one correct answer(s).
20. Half of the questions are false.
21. 9 is false. 2 is true. 1 is true, if 6 is, too.

Then, we answer some more questions based on the new questions we were able to answer:

1. Number 7 and 8 are false.
2. Four is false, twelve is true.
3. Number 20 is true.
4. One is true, two is false.
5. 3, 9, and 6, all are false.
6. I don't like strawberries.
7. Number 13 is true.
8. I like strawberries.
9. Number 5 is false.
10. Number 14 is true.
11. Number 11 is true, and 6 is, too.
12. 20 is false.
13. Number 1 and 8 are false.
14. Number 17 and 12 and 13 are false.
15. This statement is true, and so is statement 2.
16. The preceding statements are more true than false.
17. Either 11 or 15 is false, but 19 is definitely true.
18. Five and twelve are true.
19. There are more than one correct answer(s).
20. Half of the questions are false.
21. 9 is false. 2 is true. 1 is true, if 6 is, too.

At this point, we do casework

Case 1: when Number 1 is true
Case 2: when Number 1 is false.

Case 1: (This is quite easy to fill up so I'll skip some steps.)

1. Number 7 and 8 are false.
2. Four is false, twelve is true.
3. Number 20 is true.
4. One is true, two is false.
5. 3, 9, and 6, all are false.
6. I don't like strawberries.
7. Number 13 is true.
8. I like strawberries.
9. Number 5 is false.
10. Number 14 is true.
11. Number 11 is true, and 6 is, too.
12. 20 is false.
13. Number 1 and 8 are false.
14. Number 17 and 12 and 13 are false.
15. This statement is true, and so is statement 2.
16. The preceding statements are more true than false.
17. Either 11 or 15 is false, but 19 is definitely true.
18. Five and twelve are true.
19. There are more than one correct answer(s).
20. Half of the questions are false.
21. 9 is false. 2 is true. 1 is true, if 6 is, too.

Now

11. Number 11 is true, and 6 is, too.
The statement "This statement is true" can be both true and false. Since 6 is true, then 11 can be both true or false. This means there's more than 1 possible answer.

Furthermore,

2. Four is false, twelve is true.
4. One is true, two is false.
15. This statement is true, and so is statement 2.

Since 12 is true and 1 is true, then statements 2 and 4 are basically
2. 4 is false.
4. 2 is false

In this case, either one is true and the other will be false. Also, number 15 = number 2.

From the two points above, we have the following possibilities:

11 is true. 2 is true and 4 is false. 15 is true.
11 is true. 2 is false and 4 is true. 15 is false.
11 is false. 2 is true and 4 is false. 15 is true.
11 is false. 2 is false and 4 is true. 15 is false.

From these, 16, 17, and 19 should come easily.

We get the following possible true statements for case 1:

[1, 6, 9, 12, 19, 2, 15, 11]
[1, 6, 9, 12, 19, 2, 15, 17]
[1, 6, 9, 12, 19, 4, 11, 17]
[1, 6, 9, 12, 19, 4, 17]

Proceeding to case 2 (once again skipping some steps):

1. Number 7 and 8 are false.
2. Four is false, twelve is true.
3. Number 20 is true.
4. One is true, two is false.
5. 3, 9, and 6, all are false.
6. I don't like strawberries.
7. Number 13 is true.
8. I like strawberries.
9. Number 5 is false.
10. Number 14 is true.
11. Number 11 is true, and 6 is, too.
12. 20 is false.
13. Number 1 and 8 are false.
14. Number 17 and 12 and 13 are false.
15. This statement is true, and so is statement 2.
16. The preceding statements are more true than false.
17. Either 11 or 15 is false, but 19 is definitely true.
18. Five and twelve are true.
19. There are more than one correct answer(s).
20. Half of the questions are false.
21. 9 is false. 2 is true. 1 is true, if 6 is, too.

Similar to case 1:

15 is like the 11 of case 1. It can be both true or false.

Moreover:

5 and 9 are like the 2 and 4 of case 1: one is true and the other is false.

If 5 is true, 9 is false. 6 is false. 8 is true. 11 is false, 17 is true, 18 is true, 13 is false, 7 is false, 21 is true.

If 5 is false, 9 is true, 21 is false, 18 is false.
Subcase 1: If 7 is true, then 13 is true and 8 is false and 6 is true and 11 can be true/false.
Subcase 2: If 7 is false, then 13 is false and 8 is true and 6 is false and 11 is false and 17 is true.

Concluding, case 2 gives us:

[2, 12, 19, 5, 8, 17, 18, 21, 15]
[2, 12, 19, 5, 8, 17, 18, 21]
[2, 12, 19, 9, 7, 13, 6, 11, 15]
[2, 12, 19, 9, 7, 13, 6, 11, 17]
[2, 12, 19, 9, 7, 13, 6, 15, 17]
[2, 12, 19, 9, 7, 13, 6]
[2, 12, 19, 8, 17]

So I believe the total is

[1, 6, 9, 12, 19, 2, 15, 11]
[1, 6, 9, 12, 19, 2, 15, 17]
[1, 6, 9, 12, 19, 4, 11, 17]
[1, 6, 9, 12, 19, 4, 17]
[2, 12, 19, 5, 8, 17, 18, 21, 15]
[2, 12, 19, 5, 8, 17, 18, 21]
[2, 12, 19, 9, 7, 13, 6, 11, 15]
[2, 12, 19, 9, 7, 13, 6, 11, 17]
[2, 12, 19, 9, 7, 13, 6, 15, 17]
[2, 12, 19, 9, 7, 13, 6]
[2, 12, 19, 8, 17]