Measuring Current Using A Resistor?
Yes, you can use a resistor and voltage range on a multimeter (to measure the voltage across the resistor) and calculate I = V/R. That can be useful if you need to measure current outside of the range of your meter. 

For example, if you need to measure 100A you could use an inexpensive 100A shunt and a multimeter on voltage setting. The meter might read 75mV for 100A (assuming a 75mV shunt), so on the 199.9mV range you can read with a resolution of 130mA up to +/-100A. In the case of shunts, the resistance (0.75m ohm) is not usually given, rather the voltage at the measuring terminals at full rated current is given. 

In most cases you can assume the meter impedance does not affect the measurement (shunt) resistor, but not always. 

For example if you need to measure 1nA and you just have an inexpensive handheld multimeter with 10M ohm input impedance on the +/-199.9mV range you can just use the meter on voltage range as a current meter. It will read 10.0mV for 1.00nA, giving you a resolution of 10pA.