I have been to US -NJ on H1B visa for 20 days (between 21st March-2009 & 9th April-2010).

I received the W2 form which states that
$277.26 were withheld as federal tax
$283.53 were withheld as social security tax
$65.37 were withheld as state tax.

As per the IRS documents that I went through I qualify as non resident alien, since my stay has been for less than 31 days in 2009 & I have not been in US during 2008 & 2007. In which case I will have to file my taxes through a physical form of 1040NR or 1040NR-EZ.

I want to know whether I can claim a refund of all the taxes withheld, as mentioned above.

The 1040NR-EZ doesn't have any provision to claim refund for the social security tax.
1040NR has line no 63 which says excess social security withheld. Can I claim the social security tax amount in this section?
Do I also have to fill up form 843 for the same?

File nonresident tax return. On federal return, you will get exemption for $3650 plus itemized deduction.
Similarly file state tax return as part year resident.
You will not get SS tax and Medicare tax back.