How to connect different battery of same voltage level but different capacity together to supply a device ?

About all I can suggest to you is that you plan to connect the batteries in parallel (the key is "same voltage"). The capacity of the resulting array of batteries, however, is likely to be disappointing when you try to use it.

It is difficult to get batteries of different capacity to work together, no matter what you do. I assume you want to do more then just backup one phone or tablet but that you want to do something general that can be used by many different people. One way  is to put them in series and use a voltage regulator. I know, that will "waste" some of the energy but will let you salvage at least something.
You need to know more about battery characteristics including their internal resistance and the effect of rate of discharge. Almost every type of battery have different characteristic and it is HARD to mix different characteristics.
There follows here some relevant keywords for internet look up.
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battery,  battery capacity, effect of discharge rate, internal resistance (of batteries)
batteries in series, batteries in parallel, battery failure modes
constant voltage regulators, constant current requlators

Reducing waste and extending the life of old batteries is a noble goal, but any implementation is apt to present safety, reliability, and performance issues.

Lithium Ion Batteries can store impressive amounts of energy.  Energy is the ability to do work.  But from a safety perspective, energy is also the ability to do damage.  This is why it is illegal to ship these batteries by air.
     http://gizmodo.com/5985410/why-smartphone-laptop-and-airplane-batteries-explode

When a OEM is designing a series-parallel battery pack, they have the advantage of using new identical matched cells.  And they still have to be careful, generally including monitor circuits on each cell to identify problems.  And once the battery is in service, careful matching insures that the cells charge, discharge, and age the same way.
     http://batteryuniversity.com/learn/article/serial_and_parallel_battery_configurations
     http://4wings.com/lib/files/bat.pdf

Building a Li-Ion battery pack with different types of cell phone batteries is certainly a bad idea.

In fact, even with identical (same part number) used cells, the variations is age and usage history would be enough to cause potentially catastrophic failures.

Thank you all for the comments ! I give up thinking about packing the used cell phone batteries.

I think there is still a way to reuse the same voltage level batteries. We can still add a switches to switch between different batteries manually. At the device side, we can add a capacitor between the positive and negative terminal to protect the sudden power lost during the switch over. Do you think it is feasible ?

Further more, it might be possible to automate the switching action by circuits. Any comment ?

Thank you very much!

" I think there is still a way to reuse the same voltage level batteries. We can still add a switches to switch between different batteries manually. At the device side, we can add a capacitor between the positive and negative terminal to protect the sudden power lost during the switch over. Do you think it is feasible ?"
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Can it be done?  yes
Is it cost effective? No

You are connecting discarded batteries to a device.
Why were they discarded? Will not hold a charge? Just because you connect then to another device will not cause them to hold a charge. If you put them in series, the residual voltage will be higher but they will still not hold a charge or supply energy.

sadly to say - but you may classify this as a noble dream
it will never work for any sustained time; nor will it be reliable
you are only asking for problems and troubles by putting several "bad" batteries together, either way you connect them

I would like to clarify that these batteries are all good. In your countries, you would very seldom have phone with user replaceable batteries nowadays. My areas around still have many such phones. The batteries are still good but the phones are not suitable for comfortable use anymore (after some software upgrades, the phones become slower and slower......).

These batteries are not bad...... just used. Imagine some manufacturers in China have plenty stock of spare batteries of phased out phone models.

I don't not know if it is really noble to implement a switch circuit.

you are free to try, and the fact that the batteries are ok (only used) will have a positive effect on their usefulness
i suppose you would want to put 2or 3 in a box, with switches on top of them
i would then only use 1 battery at the time, - you can switch both poles with double pole switches to select one of them

There are several problems here.

The first is voltage.  You are looking for 5v from 3.7-3.8v batteries.  There are circuits that do this but you'll pay for that in current usage.  See http://www.dx.com/p/03100127-dc-dc-3v-to-5v-boost-converter-charger-module-red-154870 or Google step up converter.  Best is probably two batteries in series which would give you approx 7 volts and you can use various circuits to limit the output to 5 volts.

The second is amperage.  I don't know what amperage a phone battery can supply or whether it can supply enough to power a tablet.  You'd have to do the measurements and calculations for that.  But if two batteries in series can't do it then you going to require four batteries (or more) in series and parallel and that starts to get really messy.

The third is battery incompatibility.  You need your batteries to have the same specifications and chemistry otherwise the stronger batteries are going to kill the weaker batteries.  But this has been discussed earlier.

The fourth is connections from the batteries to wiring.  I'm not sure what type of connectors you are going to use but that is going to be messy to make.

Putting different types of batteries in parallel is asking for trouble. Even if they have the same specs, no two batteries will have exactly the same voltage. When you parallel them, very high currents will flow while the batteries try to get to the same voltage. Those currents can destroy the batteries. On top of that, even if they eventually balance without any damage, their internal resistances will vary so, once you start using them, the battery with the lowest resistance will supply most of the current, go down quicker than the others, and you're back to the balancing issue.

If you put them in series, as aburr suggested, those problems will not occur, but the overall current is limited to the current available from the least powerful battery. If you put enough batteries in series, and then bring the voltage back down, you will have a high current again. A switched mode power supply can bring the voltage back down to 5V (or whatever you need) with high efficiency. The chargers for phones, PCs, etc do that while wasting less than 1W. I would suggest putting 10 or more batteries in series to get good efficiency.

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Thank you all your information. I will think about them!