1. It seems that the two years was a long time for you.

2. It seems the two years was a long time for you.

3. It seems like the two years was a long time for you.
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Are they all grammatical? Which one is commonly used? Can we omit 'that' as in #2? Is #2 frequently used? What about 'like' instead of 'that'?

No, they are not. Two years is plural - TWO of them. The correct verb is were, not the singular was. Otherwise, all three are correct. "That" and "like", in this context, mean the same thing, but are not necessary, so #2 is also correct.