Here is a spec-sheet for the MG996R servos. Notice at the top of the 2d page, they require a supply of 4.8 - 7.2 volts, and can draw .5 - .9 Amps running and 2.5 Amps when stalled.
You'll need a supply of 6 volts (+/-) that can handle that current, times however many servos you need to operate simultaneously. The 3.7 volt batteries don't even meet the minimum voltage for the servos (unless you have two of them in series, but then they're slightly over the maximum).
You need to figure out your power budget first, then how your are going to meet it. You might be able to use a lighter supply than the worst case (6 stalled motors) would require or even than 6 motors at full operating torque (0.9 Amp each), if you monitor the current on each motor and shut down the or sequence the one(s) with the highest draw. You might even try monitoring just the battery-pack voltage, which won't tell you which motor(s) are stressing, but will let you know that you're unable to supply the total requirement for that present move.
If it were me, I'd use battery voltage sensing first (easier, simpler) to see if I have a problem that I can't solve by sequencing the motors. I might find I don't need to measure each motor's current.
So its either i use 3.7 bat or 9v. Or.can you suggest any other power
A single 3.7v battery won't work well) for a motor that needs 4.8v minimum. Two of them in series will be slightly over the max voltage spec (7.4v vs. 7.2v). Will that slight overage damage or overheat the motor? Will be OK for intermittent use? Maybe, if you're careful to shut down a stalled motor quickly. The alternative is to build a voltage regulator that will drop the 7.4 to around 6v, but the regulator must also be able to meet your power budget, too.
A 9v supply is definitely too high and will need to regulated to within the motors' spec. (I assume you're not considering the four or five cm high ones with snap-on connectors, usually used in smoke-detectors? They have very little capability to deliver current and will be totally unsuitable for your application.)
My first try would be to experiment with 1 motor at 7.4v with a typical (for your project) mechanical forces on it, and see if it overheats and how soon, with how much load. You'd be taking a bit of a risk with that motor but the potential advantage is you might save yourself having to build a high-current voltage regulator.
NiMH AA cells are 1.2V
Good call. Just know that Nickle-based batteries have the twin disadvantages of long charge cycles (or degradation of capacity with faster charging) and higher self-discharge rate of about 1%/day. Their advantage to you is that it's easier to make a battery pack whose voltage falls within the motor spec. If this is a one-time project, this may well be more important to you than their disadvantages.