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 <s> strikethrough </s> false statements and **bold** true statements.

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

Now 
>! 11. Number 11 is true, and 6 is, too. <br> 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. <br> 4. One is true, two is false. <br> 15. This statement is true, and so is statement 2. <br> <br> Since 12 is true and 1 is true, then statements 2 and 4 are basically <br> 2. 4 is false. <br> 4. 2 is false <br> <br> 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. <br> 11 is true. 2 is false and 4 is true. 15 is false. <br> 11 is false. 2 is true and 4 is false. 15 is true. <br> 11 is false. 2 is false and 4 is true. 15 is false. <br> <br> 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] <br> [1, 6, 9, 12, 19, 2, 15, 17] <br> [1, 6, 9, 12, 19, 4, 11, 17] <br> [1, 6, 9, 12, 19, 4, 17]

Proceeding to case 2 (once again skipping some steps):
>! <s> 1. Number 7 and 8 are false. </s> <br> **2. Four is false, twelve is true.** <br> <s> 3. Number 20 is true. </s> <br> <s> 4. One is true, two is false. </s> <br> 5. 3, 9, and 6, all are false. <br> 6. I don't like strawberries. <br> 7. Number 13 is true. <br> 8. I like strawberries. <br> 9. Number 5 is false. <br> <s> 10. Number 14 is true. </s> <br> 11. Number 11 is true, and 6 is, too. <br> **12. 20 is false.** <br> 13. Number 1 and 8 are false. <br> <s> 14. Number 17 and 12 and 13 are false. </s> <br> 15. This statement is true, and so is statement 2. <br> 16. The preceding statements are more true than false. <br> 17. Either 11 or 15 is false, but 19 is definitely true. <br> 18. Five and twelve are true. <br> 19. There are more than one correct answer(s). <br> <s> 20. Half of the questions are false. </s> <br> 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. <br> <br> 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. <br> <br> If 5 is false, 9 is true, 21 is false, 18 is false. <br> Subcase 1: If 7 is true, then 13 is true and 8 is false and 6 is true and 11 can be true/false. <br> 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] <br> [2, 12, 19, 5, 8, 17, 18, 21] <br> [2, 12, 19, 9, 7, 13, 6, 11, 15] <br> [2, 12, 19, 9, 7, 13, 6, 11, 17] <br> [2, 12, 19, 9, 7, 13, 6, 15, 17] <br> [2, 12, 19, 9, 7, 13, 6] <br> [2, 12, 19, 9, 8, 17]


So I believe the total is
>!  [1, 6, 9, 12, 19, 2, 15, 11] <br> [1, 6, 9, 12, 19, 2, 15, 17] <br> [1, 6, 9, 12, 19, 4, 11, 17] <br> [1, 6, 9, 12, 19, 4, 17] <br> [2, 12, 19, 5, 8, 17, 18, 21, 15] <br> [2, 12, 19, 5, 8, 17, 18, 21] <br> [2, 12, 19, 9, 7, 13, 6, 11, 15] <br> [2, 12, 19, 9, 7, 13, 6, 11, 17] <br> [2, 12, 19, 9, 7, 13, 6, 15, 17] <br> [2, 12, 19, 9, 7, 13, 6] <br> [2, 12, 19, 9, 8, 17]