I'm a tourist in NY, if at the airport they check my luggage when I'm about to come back home (European Union) will I have to pay any custom duty, tax, or whatever?To be more specific, the purchases mentioned in the question are an iPod (paid $249 + VAT = $268.92) and few cheap souvenirs.

I don't think so. You've already paid a tax for it, and it's not as if you bought it from a duty free shop where there would be no tax if you only use that product in the place you're traveling to.