lithium-ion is nominal 3.6V per cell, BTW
If you want to charge 4 batteries, you need a charger that can deal with 4 batteries in different states of charge. I don't personally know how the consumer chargers do that. You are better off with a larger single cell battery pack and a boost converter. Also, if you over-discharge a li-ion cell it is destroyed. Some li-ion battery packs have built in protection circuits.
If you overcharge a li-ion battery it explodes or catches fire. Very dangerous technology.
Properly charging LI-ion batteries is non trivial. They start with constant current charge until they reach 4.2V +- 10mV, and then you reduce current to maintain 4.2V until the current becomes very small. You can imagine trying to do that for 4 batteries in differing statesw of charge.
To create a "USB Compatible" charger is also not trivial.
Also, getting a cellphone to charge is not trivial. Many will only charge if connected to a charger that obeys the correct charger protocol. Iphone, nokia, etc are all different. Look at figure 3 (page 16) in this datasheet.
http://datasheets.maximintegrated.com/en/ds/MAX14578AE-MAX14578E.pdf. It show what is needed to fool different phones into charging. (usually shorting DP to DM is adequate)
After you solve the battery charger issue, you need to create 5V +- 5% power supply or the phone won't chage. And, depending on the phone the current demand can be from 500ma to 1.5A.
You should buy a commercial pack to do what you want for the phone you own. Robust, tested with the phone, etc.
I make battery chargers, and I would not build my own due to packaging, reliability testing, etc. You won't be able to match a commercial solution for ruggedness and abuse.
BTW, The TI bq2000 chip has a design example for a single li-ion cell in figure 7. Not sure how to expand that to 4 cells. It also describes the 2 stage (actually there are three) charge algorithm for li-ion.