How to politely decline a postdoc job offer after signing the offer letter?
Joining the other commenters: I'm not sure what you think a "commitment" is if signing an offer letter and having your employer issue a visa do not qualify!

I'm not sure why you think that your answer in the interview is relevant: it is perfectly normal for you to consider other positions until you accept one, at which point you should take yourself off the market.  

I think it is very likely that the offer is not legally binding: I have seen such things happen to departments, and they have never pursued the matter legally.  What will happen though is that the people who offered you the job will feel that you reneged on them, and in particular that you broke your word.  That they have gone to the time and expense of successfully getting you a visa is likely to amplify their feelings of ill will.  (Also, it could make them be less willing to hire foreign workers needing visas in the future: please think about the implications of that for a while.)  It is possible that this could damage your academic and professional reputation in the long-term with this faculty member, at this university, and perhaps in broader circles containing them.  It is also possible that they will get over it rather quickly and hold no lasting grudge.

If you want to renege for a permanent academic job in a country that you distinctly prefer living in: in my experience, while some will call that action dishonorable, most will ultimately countenance it as something that you needed to do in order to get the happy life you want.  But if this is a temporary job for which you cannot see your way to your next job or staying in the country you want to live in: this could turn out to be a decision that you regret.  Whatever you do, I certainly urge you to get up to speed on how academic hiring works: this will stop you from making serious mistakes in the future (and may convey other advantages in your future career).