Last month I was traveling to Japan with my husband and my brother in law for visit from USA. Immigration officers let my husband and my brother in law entry into the country,but they not let me in due absence of visa. My question is who’s responsible for this? Do airline for this?
You are the only person responsible for ensuring that you have proper visas to enter a country. While many airlines flying to some locations ask passengers if they have the correct visa before they fly, the airlines do not have to do this [edit, they do, but that is an obligation they have to the destination country, not the traveller, and travellers are due no compensation if a mistake is made]. Before you travel anywhere you must check your destination's visa requirements or this will keep happening to you.
You can't sue the airline.
Check your documentation that you received when you booked your tickets. You will find somewhere a clause that explicitly states that you are responsible for ensuring you have all the required documentation for your trip, including any visas that may be required.
You haven't said what happened after you were denied entry, but I imagine that the airline flew you back to your point of origin. The airline will have incurred costs in doing this, and they might also have been fined by the Japanese authorities. It's possible (but I don't know how likely) that they might come to you for the money.