POWER FOR SOLENOID VALVE

I hadn't thought to deep about this before, but I must agree with shabaz as a solenoid has no way to create a counter electromotive force - which is what creates the current reduction in motors.  There is also no inductive reactance since it's DC.  There is probably an instant of subtransient reactance during the initial energization but since there is no frequency, it's theoretical at the speed of electrons level.

We may experiencing one of the challenges in our field - language / terms / nomenclature.  Solenoids can be the single coil relay thing or they can be the pull-in coil / holding coil variant.  Sometimes the latter solenoids have 3 wires.  These may or may not have internal contacts to drop out the pull-in coil.  The 2-wire variant will always have contacts to disconnect the pull-in coil at the end of travel for the solenoid.  The pull-in coil is used to overcome the Law of Inertia and will definitely burn up if left energized - because it has low resistance.  Magnetism in this case is all about Amp-turns with an emphasis on the amps.  We get the high impulse to move the armature but we don't need that much energy to keep it centered in the holding coil.  The holding coil is also about amp-turns but the emphasis is on the turns; thinner wire, more turns, higher - current limiting - resistance.

SO... solenoids can appear to have inrush - but they don't.

Agree, hard to see how that condition could be defined as inrush, (e.g. it would be called a stalled condition for a DC motor, don't know what one would call it for an AC solenoid!). Also reminds me of an old discussion (with a blog from John Wiltrout from memory) where it was discovered that impedance could be lowered in some conditions (depending on the particular metal, and the AC frequency). Granted it's more likely to be 50/60Hz here.

They do create counter EMF each time they move.

    This is my solenoid valve voltage rating

your valve works with 230V AC, it will not work (to specification, if at all) with a 24V power supply

And you could make yourself a science experiment to see why this is the case. Get an electromagnet (any electromagnet, could be a relay coil, or a spool of wire) and by applying different voltages, try to approximately see what difference in force you're seeing. Try half the voltage, then a quarter of the voltage, and then a tenth of the voltage. What you'll  observe will make it very clear.

shabaz to be clear can you emphasize me the causes of solenoid valve not function when testing? Can you advise me the solution to these problems/causes?

The electronic portion (assuming it is a solenoid version and not a motor) is just a coil of wire, so ordinarily that could outlast a lifetime, although the winding can get damaged. You can do a very basic, very partial test by checking with a multimeter to see if it has gone open circuit. Other than that, the item is mechanical, so there can be plenty of mechanical problems (accidentally knocked plunger, stuck plunger due to dirt, etc. 

Since it is a gas safety valve, it's best to replace it with a new modern one. Otherwise, if it ever fails and there is damage or someone is injured, the person that repaired and re-installed it will be the one that will be imprisoned.

Obviously that's an expensive part, but if you're just looking to experiment with a solenoid valve (and don't intend to install it in it's normally intended application) you can get plenty of small low-voltage (e.g. 24V) devices for very little cost.

Is it possible to fix and repair the plunger that being dirty or rusting? Because when there have gone open circuit, the voltage and Amp is enough, and have supplied but the solenoid valve cant trigger to close valve. 

Personally I think no, it should be thrown away in a condition that no-one repairs it. I know there's a strong desire to repair and re-use, but in a critical application the $100 is not worth the risk to lives (and there would be a high risk). Everyone knows of gas explosion stories in their own towns or neighbourhoods, so it's not rare for things to go badly wrong. This would increase the risk a lot.