Can I plug USBasp to an outlet via cellphone charger adapter and therefore power my standalone ATmega328p?
You could, but it makes more sense to ditch the USBASP AVR programmer between the USB charger and the ATmega altogether, and power the ATmega from the USB charger directly. The USB supply voltage is 5 V, just what the ATmega needs. 

If the charger has a removable cable you can just take some old USB cable, cut off the slave side (B, mini-B, micro-B) connector, remove the insulation and hook up the GND and Vcc (5 V) lines. The data lines should be left unconnected.