The USA does not mind.
You buy the phones, you pay what is needed and put them in your luggage.
TSA, the airport security people will ask you to put all phones through the scanners, no problems there.
4 phones is many but there is no legal limit. Carry-on luggage is the right place, not hold luggage, due to batteries in the phones.
In Rome, if you do not need to collect your bags and hand them in for the new flight, you will likely not see customs. Immigration are the people who will ask you for your passport, customs are the people who check whether you bring in illigal items, or need to pay a tax on it.
When you arrive in Albania you will need to go through customs, this is where you run the most risks.
There will be a maximum amount of value you may import into the country without having to pay import tax and 4 new phones are very likely over the limits.
Four second hand (or one new and three second hand) phones are more likely acceptable.
Keep your paperwork from when you bought them, showing the price you actually paid. Based on this and on what the customs people think they are worth they will work out whether you can bring them with you or have to pay.
Best is to go to the 'I have something to declare' line and ask the officers. It makes sure you have to pay if you bring too much but you will not get into problems.
The more risky thing is to just walk through the 'nothing to declare' line and hope they do not ask you.
If they do check you, you can be sure that all 4 phones will be found, also the two in your pockets. And in that case you will likely need to pay a fine and might have to hand it the ones that are over the limits.
Before you buy the phones you should look into the amount you are allowed to bring into the country.