The dog has almost gone blind. He said, 'It's strange. These days you look blurry.' (You refers to the dog's master.)

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What does 'it' refer to in 'It's strange'? Does it refer to 'situation'?

I don't think there's a specific antecedent for "it" in that expression. Its use is similar to the use of "it's" in the following:

It's raining hard right now.
It's really dark outside, isn't it?
It's 99 degrees and humid outside.

The impersonal "it."