I had traveled to US, California on an H1B visa in Jul '05 and returned in Mar '06 to my home country in India, thus I was in the US only for only 3 months in 2006. My gross income was just over $16000.00 for 2006 with taxes of $2500.00 paid as Federal tax; and $900 as State Tax.

Is it possible to claim all the taxes back as refund for 2006 for me or do I owe the government any taxes? I don't fulfill the 183 day rule so I guess I will have to fill the 1040NR form. I was single in 2006 and my wages were my sole earning.

Please advise.

You will file form 1040NR or 1040NR-EZ and pay taxes as per your tax return. There is no way you can claim all the taxes for 2006.
For 2006 your taxable income is $16K minus $3300 minus $900 = $11,800. Your federal tax will be around $1400. You will get federal refund of $2500 minus $1400 = $1100.