To program them try following this guide. Out of the box those ESC's apply a low-pass filter to the signal, which should be disabled. You can also try to advance the ESC's timing to drive the motor harder/faster. This can be done with just your Flight FC and going to the motors tab. Make sure motors are powered and props off.
So ultimately your problem is that your setup cannot convert the power from your battery into thrust/lift effectively. This is a classic Power Transfer problem. caused by poor impedance-matching; Like driving a car in 2nd gear on a highway, powering a 120V toaster with a car battery, or riding a bike in too high / low gear.
In fact, there are 2 impedance matching problems here: Between the motor and battery voltage, and between the motor and propeller size. The motor is just a transformer that converts voltage into RPM, and the current it draws depends on how much torque the motor is delivering into the mechanical load. i.e; the propeller. The KV rating is analogous to gearing within the motor.
For a good flying quad you need 5 to 10 times more thrust than the weight of the craft. and you can't acheive that with your current setup. To do this you need to pull more power from your battery. With a 2S or 3S your voltage is very low, and the KV rating of your motors is low. The maximum speed is VERY limited. However you probably some unused margin in the current you can safely pull out of the LiPo.
Fundamental ways to improve performance:
Option 1:
Larger props would give more lift at lower RPM, at the cost of more current draw since larger propellers require more torque at a given speed. This will only help a bit, maybe 20% with the props linked below. These motors are designed to be used with 7" to 10" propellers. Larger/slower propellers will also add lower frequency higher amplitude vibrations and will introduce jello into cheap cameras if it's hard-mounted. Try these propellers.
Option 2:
Get motors optimized for a 5" build. There are plenty of 2204, 2205, and 2206 motors out there, just get the cheapest ones, about $35. You can try to re-wind the motors to have a lower electrical impedance and kV.
Option 3:
2S isn't enough. I think your build will struggle to hover with a 2S. I wouldn't even be surprised if it can't lift off the ground.
3S is barely enough. It might hover fine (especially while the battery is fresh) but once the voltage drops to around 11V, I suspect it will struggle to maintain a hover and have very sluggish acceleration, you will not have enough throttle to control the aircraft in any sort of maneuver. You will grow tired of just hovering around.
4S might be enough all else equal, but it will still be a poor performer compared to modern builds. With 2300kV motors it is enough for free styling.
5S to 6S: Generally reserved for skilled pilots who want to launch to the moon in 200 milliseconds. With very good quality components and a battery capable of delivering thousands of watts, you can go as high as 2700kV with larger motors that can dissipate the heat and have this ridiculous build but generally lower kV motors are used for such setups. Note that this pushes current technology (power density of Lithium Ion Batteries, power dissipation capabilities of BLDC motors) to the very limits and is very much experimental. Expect fire and smoke when pushed too hard for too long.
Option 4:
ESC's are quite complex, and the ones we use for the hobby are electrically simple and are not capable of boosting the voltage much. Professional VFD's do sometimes have some limited capabilities... So it's not really an option unless there is a software limit set to the maximum RPM, torque, power, current, etc. that should be disabled.