According to National Electrical Code, the pipe has to be bonded. However, it can be bonded using the grounding conductor serving the equipment that uses the gas.
...The equipment grounding conductor for the circuit that is likely to energize the piping shall be permitted to serve as the bonding means...
As for lightning strikes, the gas company is probably correct. It's not likely lightning will strike the pipe, especially since it's right next to a house.
National Electrical Code 2014
Chapter 2 Wiring and Protection
Article 250 Grounding and Bonding
250.104 Bonding of Piping Systems and Exposed Structural Steel.
(B) Other Metal Piping. If installed in, or attached to, a building or structure, a metal piping system(s), including gas piping, that is likely to become energized shall be bonded to the service equipment enclosure; the grounded conductor at the service; the grounding electrode conductor, if of sufficient size; or to one or more grounding electrodes used. The bonding conductor(s) or jumper(s) shall be sized in accordance with 250.122, using the rating of the circuit that is likely to energize the piping system(s). The equipment grounding conductor for the circuit that is likely to energize the piping shall be permitted to serve as the bonding means. The points of attachment of the bonding jumper(s) shall be accessible.
One of your appliances has a ground fault
It often comes as a shock to people, but sometimes their appliances have a defect. Its internal electrical insulation isn't up to snuff, and it is leaking current (typically from the "hot" wire as neutral is usually harmless). If the leak is small, it may self-limit current to feelable but non-lethal amounts. Such leakage tends to get worse, so what tickles today could kill tomorrow.
Essentially, the insulation failure and the human become a resistor ladder as both are resistors and both are in series. So the amount of the insulation leakage, and the quality of skin contact, determine resistance, and thus the amount of current. Do it again with wet hands and now your resistance is much lower and you're dead.
As such, any tickle should be considered extremely dangerous and repaired with extreme prejudice.
DVMs (Digital Voltmeters) are not 100% reliable. Their resistance is so high (in theory they should read a fault as full line voltage) that they often misread ordinary capacitive coupling as relevant voltage.
Don't use yourself as a voltmeter. Hunt down a testing device that successfully indicates the fault, e.g. a non-contact voltage tester, mechanical meter voltmeter, neon light tester, etc.
GFCI/RCD is a starting point
If you want to get personnel protection in place tout suite, which I most definitely recommend, then install a GFCI aka RCD device powering either the offending circuit, all nearby circuits, or the whole house (which is the usual approach in Europe). An 8ma threshold GFCI/RCD will provide personnel protection. A 30ma threshold will provide limited personnel protection, it can still kill, especially by a stun causing a drowning or fall.
Hunt it down, one appliance at a time
Now you need to move through each of your loads, and see which load or device is causing this. You can start by shutting off one circuit breaker at a time, and see which one extinguishes the effect.
Once that's the case, note which devices are offline with that breaker off, and move through them one at a time.
Very rarely, it can be something totally out of left field. I have no idea how to advise patrolling for that.
Best Answer
First off you should tell us where you are on the planet in order to get accurate answers.
1)There are 8 grounding points in the drawing. Which of them should be bond together?
All of them should be bonded so that they are at the same potential.
2) How many grounding rods I need?
There should be a minimum of one ground rod per location and possibly two. If all this equipment is in the same location two should suffice. If it is spread out over a large piece of property then I would judiciously add more rods. There is no exact answer here.
3) Where should I connect the Neutral Line to the Grounding Rod?
As close to the main service panel as possible.
Good luck!