I have permanently moved back to my home country after working for 10 years on H1B. My questions are:

1) Do I have to pay a penalty on early withdrawal on H1B. Do I have to pay Illinois state taxes if I withdrew after moving back to India
2) Do I get to deduct moving expenses, etc

Thanks

1) Assuming you speak of the 401K or IRA you opened while in the U.S. The answer is YES. If you withdraw from either the 401K pr IRA before you are 59.5 years of age, you WILL owe the 10% Early withdrawal Penalty.

2) You cannot deduct moving expenses moving back to India UNLESS you continue filing U.S. tax returns after you return to India.

Yes, for 2016 I will be filing Form 1040

Also, if you left the state of Illinois, then did the withdrawal, then Illinois has NO legal standing to tax the withdrawal.

So for 2016 can I claim moving related expenses related to moving back to my home country?

The US-India tax treaty has some benefits if you take it out in periodic payments.