Measuring Li-Ion Battery voltage during charging/discharging
You must limit the maximum charging voltage to 4.2V, or else the battery will explode! When you do this the charge current will naturally taper off (once it drops below 10% of the original charging current you can consider the cell to be fully charged). At normal discharge rates the cell will be almost completely drained when it reaches 3.0V. You may get a bit more out by continuing down to 2.75V, but also risk damaging the cell. 

The energy efficiency of the cell is the ratio of energy extracted during discharge to energy input during charge. To get correct results you must use the actual terminal voltages measured during the test. Compensating for differences between charge or discharge and resting voltage will remove the very thing you need to measure - energy lost inside the cell.  

Where you may have a concern is how to ensure that the start and end points are the same for both charge and discharge. Since discharge voltage is lower than resting voltage, if you charge the cell and then discharge it you don't know whether you have taken it down to the same amount of charge it had originally - perhaps it was already partially charged and you took out more than you put in, or perhaps the discharge cut off early and you didn't extract all the charge you put in. 

The answer is to first charge the cell up fully to get it to a known state, then discharge it, then recharge it again. The discharge end-point may vary depending on current drain and temperature, but the charging end-point will always be the same.