for 'singular thing':
1. I wouldn't want this/that.
2. I wouldn't want anything like this/that.
for 'a specific thing':
3. I wouldn't want this/that house.
4. I wouldn't want a house like this/that.

for 'plural things':
5. I wouldn't want these/those.
6. I wouldn't want anything like these/those.
for 'specific things':
7. I wouldn't want these/those ties.
8. I wouldn't want ties like these/those.
9. I wouldn't want ties like this/that.

Which of the above examples are grammatically considered correct, considering you're speaking for your own opinion of disliking something or some things.

Thank you very much.
They are all correct. Whether you use this/these or that/those depends on your proximity to the object(s) in question. If you are close use this/these not so close use that/those. What is close? Good question. See this site for guidance (I'm sure there are many similar sites):
Wow, that means even #9 is correct?
If so, in what situation?