How to know if a vehicle is moving without any external source of information? The situation is the following:
I'm inside a vehicle (plane or a car, it doesn't matter) and I need to know if the vehicle is moving at a constant speed BUT I cannot perceive any external change like visual changes, vibration, etc.
How can I know if the vehicle is moving? Do I really can know?
Additional question Can I know my speed?
 A: Actually special relativity states that all inertial reference frames are equivalent, so there is no such thing as absolute speed. 
You can't ask "What is my speed", this question is just not well formed. You can ask: "What is my speed in reference to this object", and in fact all "real life" examples of asking "What is my speed" actually have some implied reference frame. Traffic sign specifying that maximal speed is 50 km/h, reall specifies that: "Maximal speed of car in reference to road surface is 50 km/h". 
In case of moving on earth you allways have a handy reference frame (that is: earth) and you can measure: 


*

*Your speed in reference to air. 

*How fast wheels of your car are moving. 

*You could measure speed using GPS


Without Earth as reference frame (or some othere reference frame) this question has no answer. This is because special relativity postulated (and we have experiments for that!)  that there is not "special" reference frame that "is not moving". 
Before Einstein it was assumed that there is a special medium named ether, that would be that special reference frame, and if this was the case you could always measure your speed in reference to ether using simple physical experiments: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment . 
A: You cannot tell moving with constant speed apart from standing still. This is the principle of Galilean relativity.
A: As an abstract spherical-chickens-in-a-vacuum-type question, then no, basic relativity says not.
But that isn't much fun. ..
First up, what do you mean by speed? If you mean speed along surface of earth then you have a chance.  Since the earth is curved you are always accelerating, and you could measure the drop in g as you speed up. So long as you don't go fast enough to go into orbit... Of course the is some degeneracy between speed and altitude for this.
Of course. If we are moving on a true straight line it is easier still as you will move through the earth's gravity as you pull away from the surface. Or burrow beneath it! 
A more practical method (that is actually used) would be dead reckoning.  If we assume (or assert!) that the vehicle was stationary when you got in then you can in principle detect every acceleration the vehicle makes from then on.  Integrating these will give you your current velocity. Of course the accuracy of this method decreases with time as the errors simply accumulate. 
Finally, if our vehicle is ground based, then an oddity of fiction could at least tell us if we are probably moving or stationary. Friction between surfaces is typically very different for static and dynamic friction, with static being stronger.  This means that when something slides to a stop (be it a sled or break discs) it almost always jolts slightly at then end as the stronger static fiction kicks in. You will feel this on buses and trains frequently. Although careful control can minimise the jolt, looking out for it with a sensitive accelerometer would give you a strong hint you had stopped.
A: If you had some type of gravimeter you could check whether local $g$ were changing. If so, you might reject the idea that you're stationary and infer that the variation in $g$ is due to you moving over different parts of Earth. This would require your hypothetical vehicle to be pretty darn smooth, though.
It's important to state that the reverse situation is not true: A constant $g$ would not necessarily imply you're stationary.
Note that this does not violate Galilean relativity since the laws of motion are still the same; you're just detecting the spatially-varying gravitational field by moving through it.
A: Assuming that you know the gravitational field in the area you're passing through, you can determine whether or not you're moving at a constant speed (which I take to mean "stationary in some inertial frame") by whether or not you're feeling gravitational forces other than what you'd expect from the field.  For example, if there is no gravity and your scale says you weigh 10 pounds, then you are not moving at a constant speed.  
A: Does humidity and similar cues count in the answer or not? 
For example if moving continously after a while certain environmental parameters will change. Which cannot be screened in the vehicle.
For example humidity, temperature etc.. 
Assuming the vehicle can actually screen all those parameters. Then one can use non-inertial cues: For example rotations, turns, acceleratios etc..
Assuming no non-inertial cues are present, then as already stated, the principle of relativity (for inertial frames) makes the uniform motion and no-motion equivalent.
A: Are you traveling in a vacuum?  If not, use a pitot tube
A: Acceleration
If your exact need is, as you say, to determine "if the vehicle is moving at a constant speed" then there is a wide range of accelometers available on the market with various degrees of accuracy.
If the accelometer shows 9.8 m/s2 downwards (assuming you install it in a fixed orientation relative to the vehicle), then it is moving at a constant speed (possibly with a constant speed of 0 relative to the ground), if it shows anything else, then it's speed of movement is not constant. 
