What do you think, is it beautiful or not beautiful? –Sorry, I do not
have strong feeling for it.
I doubt the use of “strong feeling” is not perfectly right here, because to have strong feeling for something is equal to “to like something very much”. Usually, people like beautiful things, and dislike ugly things, but to answer the question about whether it is beautiful or not with “I like it or not like it” is a little bit question-begging.
Best Answer
You can't have "strong feeling" in this way, because feeling here is an ordinary noun. You must have a feeling or plural feelings. Fortunately, strong feelings is a set phrase.
An idiomatic conversation might be:
Note the omission of the last "beautiful". It's implied in the not; you don't need to repeat it.
The respondent uses the set phrase "strong feelings". The feelings need to be qualified in some way, and "one way or the other" is a set phrase which refers to the two alternatives offered. You could say "I don't have strong feelings about it."
Note that having feelings for normally refers to some sort of affection. If you have feelings for someone, you are attracted to them. Having feelings for some thing might be misinterpreted. If the conversation was about a sheep, for example (a sheep might have a particularly beatific facial expression), you don't want to say you have feelings for it!