Can I use another countries currency (gift card) if I live there but have a US based address?

there's nothing you can do, you must use the store in the payment methods available in the country you are currently in

Did you purchase your gift card locally? Are Euros used in Ireland (sorry, I don't know that). Currency cards can only be used to purchase items in the country that they are sold in. For example: You live in Belgium and purchase a currency card locally
but your gamertag is set to Ireland. The currency card can only be used if your tag is set to Belgium.

Hello btc,

We understand that you have an inquiry in regards to an Xbox gift card.

Unfortunately, buying an Xbox gift card
in any country would mean using that currency within the same region. This is mentioned within the linked page:

• Can I send a gift card to another country?
  Gift cards are in local currency, so when you buy a gift card it will only work in the country where it was purchased
  

We hope that this information has helped, and we wish you the best!

You cannot move currency between countries, this against government and commerce regulations. You can only purchase gift cards for your currency in your country and you can only use your current currency on your account. Do not try to change regions
on your account to use a gift card, this may cause serious complications with your account. Microsoft will not reimburse for a card that is not the correct currency.

Sorry to hear it. A gift card does not change it's currency based on where you live. If the card you redeemed was posted to your account in US currency then that's the card that was given to you. I would recommend contacting the seller to see if there's
anything they can do to help.