@Faysal Alam - You've gotten a lot of advice but one thing I haven't heard is - Use the situation with your parents as your strength, not as a weakness! If cultural (and girlfriend!) allows or even encourages it, then take advantage! You have 3 other people in your immediate family that will follow your lead, as the first generation english speaker and from what it sounds like, the financial head of household. This is an incredible boon to someone so young! I am jealous.
My advice - find a community outside of NYC that supports your parent's native language. There has to be other areas, cities even, that support a neighborhood of folks that speak the language - even moving from NYC to an area like Orlando would cut your spending dramatically. Orlando is a large melting pot and your aging parents may enjoy the warm weather on cold NYC bones. They may make more friends that are closer to their age. Most cities area cheaper than NYC - so take your time to do your research and see if you can get out of NYC, maybe leverage your position as the head of household. I realize that a crux of older cultures is that the elders are always in a leadership position, but your situation may be different and don't want to presume.
If you absolutely cannot leave NYC, maybe you can move just outside NYC? There are a lot of ways into the city - boat, train, bus, and each increasingly cheaper. Can you work outside of NYC in a similar environment? Say you are a restaurant server, can you serve in a nice place in a cheaper location?
With the move, you may need to coach your parents into a lifestyle that doesn't require the luxuries of the city. As you are finding, everything comes at a price and to get ahead and for you and your girl to build a life together, you may need to give a bit of that luxury up today to set your family up for tomorrow. Can your family still commute into the city on the weekend to see native-tongue friends? Can you teach them how to Skype, email, text, Google Duo, or Apple Facetime? Or maybe they just pick up the phone and give people a call.
Just some ideas my man. Best of luck!