Short answer to key query:
Battery charging energy efficiency can be defined as (energy out)/(energy in)
Energy in can be measured across a complete CC + CV charging cycle by measuring charging power per unit time throughout the charge cycle and summing the readings.
For example, if voltage and current are measured at one second intervals then
V x I = Watts and in one second there will be V x I Joule input.
Summing the once per second readings across the whole charging cycle gives Joules input.
If measurements are made every say 0.1 S then Joules per reading
= 0.1 x V x I or more generally
Joules = t x V x I
where t = time period, V = average Volts and I = average amps during period t.
Obviously I & V should be as 'steady' as possible during period t. For say 1 second readings, during the CC phase I is constant by definition and control and V will vary from about 3V to 4.2V in about 40 minutes.
So voltage increase per second will be about (4.2-3)/(40 min x 60 secs/min) or about or about 0.5 mV per second on average or about 1/2400s = 0.04% of total variation per second.
ie once per second readings are liable to be entirely accurate enough.
Much useful information is available from the Battery University website
-see "What's this Battery University stuff?" at the end of this answer for comment.
It has been asked whether it is possible to measure SOC initially without coulomb counting. There are "special" methods available such as the use of GMR sensors embedded within the cells to measure magnetic properties which are a function of SOC, but the ability to do this requires specially modified cells and special equipment.
This method is described on Battery University page How to Improve the Battery Fuel Gauge
and also here
If you wish to know the SOC initially you need to say why it is necessary and desirable to you to do so. Otherwise people could go to vast effort trying to answer with no certainty that they were addressing what you thought you needed.
Many manufacturers require users to do an initial long charge.
This is in many cases not really needed but it does allow setting the upper coulomb counter boundary with some certainty. Why should YOU be special ? There may be a good reason, but if so you need to say what it is.
You have read all the best material you can find. You ask for an EXACT SOC 1st off in the middle charge range. You KNOW this is impossible. Why do you ask for it. Why does it matter?
A good reason that mid range SOC is not able to be determined on a newly inserted battery is that factors which are unknowable may apply. The battery may be new, or slightly used, or very used. This matters. If this is not a factor and all the batteries will eg be new you should have said so. Not saying so presents a distorted problem. If the past use is unknown then the SOC is unknown and the problem is again distorted.
You could make attempts to pulse charge or discharge the battery to see the effect.. But you don't know the mAh capacity so the effect will be uncertain. But, maybe you do know the mAh capacity - but if so, you did not say.
The battery maker will be unknown - which matters. Or maybe this is not true. But, you did not say.
The manner in which the battery was recently charged and discharged also matters. If the battery was very slowly charged to constant voltage and then allowed to charge to say only C/20 before charge termination it will be very close to full capacity and this will be reflected in its voltage change under load subsequently.
For practical purposes the SOC of a good condition battery of a known capacity made by a known manufacturer when tested under known conditions after having been charged with a known profile will be able to be estimated to within 5 to 20% of actual. 5% would be lucky and 20% unlucky. Good and bad luck happen. If you need better than that and it's crucial, you could use a bigger capacity battery, so that it matters less.
Is it possible to measure a LiIon battery's energy efficiency, even if I charge it properly (i.e through both CC and CV cycles)? ie so it's not necessary to charge it ONLY in CC cycle and NOT in CV cycle?
Efficiency of charging can be measured in at least two ways.
Current efficiency is measured as ( mAh out / mAh in).
This should be measured under predetermined charge and discharge conditions.
Under typical charge and discharge conditions LiIon cells have close to 100% current charge efficiency. Unlike some other battery chemistries (such as eg NimH) there are no secondary reactions to "eat up" charge current.
Energy efficiency is measured as Wh_out/Wh_In (Watt hours out / Watt hours in).
Energy efficiency is good compared to many other chemistries but well down on current efficiency. Energy efficiency can be measured by summing Watt seconds of charge and discharge. In practice, measuring voltage and current every say second, calculating watts = volts x amps and summing the result gives accumulative Watt seconds.
When SOC is relatively low, at charge rates of C/1 or less Vin under charge and Vbattery if charging is stopped at a given moment, or even Vbattery under discharge at the moment are all similar. Vbattery_charge will be ~= Vinternal + Icharge x Rinternal and Vdischarge will be about Vinternal. As SOC approaches the point where CV mode charging starts Vcharge starts to get ahead of Voc and not all energy is stored and energy charge efficiency drops.
The following is probably more interesting than useful or practical but indicates that early charge termination is likely to give higher overall energy efficiency.
The diagram below from Battery University application note BU409 Charging Lithium Ion is probably quite wrong at a detail level but useful in illustrating the process. To see what is happening on the graph it is important to follow all 3 of voltage (small dashes, left hand axis, current (larger dashes, right hand axis) and capacity - solid line with no y-axis formally assigned but assume it's an 1800 mAh cell and use right hand axis (mentally) labelled as mAh. Charging is carried out at CC from start to B and at CV after B.
From start to A voltage rises rapidly and the capacity curve will be wrong (should have low slope to start) - but little capacity is involved. Importantly, from A to B capacity and voltage both rise approximately linearly.
This is likely to be an area of high efficiency with loses mainly being Ichg x R internal.
CV starts at B and the inflection point in voltage and current probably should be at the same time so the graph is somewhat suspect. From B to C the capacity slope is lower and after C it's lower again. Point C is probably not a sudden sharp change as shown and (capacity increase)/watts will fall across this range. There is no easy way to plot what the actual wattage capacity increase is using normal test methods. Battery university describe the use of GMR magnetic sensors in the cells to measure SOC but short of that you'd need to conduct a number of runs and discharge the cell after a range of different charge periods and see what capacity has resulted. (More complex partial discharge methods may work).
"What's this Battery University stuff?"
Battery University is the self assigned title given to a collection of battery related webpages provided by Canadian company 'Cadex Electronics'. It's not a university and it's just one of many many battery information sources on the internet.
However, it's one of the best single sources for a wide range of information on a wide range of battery types and related issues. Quality and accuracy varies but is usually good to excellent, and is essentially never terrible or highly misleading. If you want to know anything about batteries it's a good place to start and in many cases may be all you need. Technical level is not deep and if you want advanced theory there are many other places to look. But, if you want a good place to start, in most cases this is probably as good as any. (Many other sites think so too - I often enough find material which is clearly copied directly from the BU site without attribution and often enough with the implication that it's their material. I once contacted BU about a flagrant unattributed mass copying of their material. They were surprisingly unconcerned - 'getting the knowledge out there' seems to actually matter to them.
I have no association at all with Cadex except as a user of their very useful website.
You'll find that quite a lot of the things I say about battery matters match what is said on the battery university pages - as you'd hope. Some of it comes from there (which I give a link to if it's specific), much from 'all over', and various amounts from my own experience. After a while it all get's mixed in together as part of one's sum total of related knowledge. I try to be sure that anything from anywhere that I quote or state is consistent with my understanding of how it all fits together.
Learn about batteries main index page.
BU409 Charging Lithium Ion
BU907 Testing LiIon batteries
BU208 Cycling performance - LiIon and others
BU-206a Finding the Optimal Runtime and Power Ratio of Li-ion
How to Improve the Battery Fuel Gauge
Battery Fuel Gauge: Factual or Fallacy?
BU-903: How to Measure State-of-charge
BU-802: What Causes Capacity Loss?
BU-802a: How does Rising Internal Resistance affect Performance?
About - history
Here are some prior answer of mine on stack exchange EE that relate.
You can find these and others like them by searching with appropriate search terms.
If there is anything you need to know that is not covered here please [ ask :-).]
Those marked - 'with "Battery University" reference' have relevant external links.
Lithium Ion Battery Charging Practices
How to Calculate the time of Charging and Discharging of battery?
What parameters affect battery charge time?
How fast can a Li-Ion battery be charged?
Reading a Li-po battery's remaining charge
how to measure state of charge of a battery through algorithm?
How deep should we discharge lithium batteries to maximise their lifetime? - with "Battery University" references.
Is it safe to have 4V continuously supplied to a lithium battery?
Effects of continous slow charge on a battery?
Maximum *charging* voltage for Li-Ion battery - with "Battery University" references.
Full Charge Indicator