I am using a 150w HPS/MH ballast, with 150w lamps. But when I tried my two 150w G12 lamps, both didn't strike despite being brand new. Both were glowing on tesla coil but on ballast, both showed slight dim arcing. Even with the tesla coil's aid, they are not starting. What should I do?
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You might have a weak ignitor.

My ignitor strikes all 150w lamps, but why not the G12 ones?

Weak thin spark in the lamp may mean a weak ignitor / reluctant lamp, but also may mean a circuit break somewhere in wiring or lampholder! A frequent appearance with RX7s lamps when one end did not fit properly.

I tried connected the lamps directly to the ballast terminals (perfect spacing), but it still didn't work.

Also I have some Osram G12 lamps (old school single ended tin halide) that probably sit in storage for many years, when first energized, these show a weak spark discharge for quite some time, 1+ minute, then suddenly transfer to a proper high current arc.   

One of them is producing a weak spark when I put my hand near it, while the other is doing nothing. Can I give them a 'boost' by using a higher wattage ballast?
I also tried a stronger ignitor, but it doesn't help.

Higher wattage ballast does not necessary means higher energy or higher voltage ignition. May be this lamp has some internal contact broken, at the base, or in molybdenum foil leads. Let it sit for some time igniting.


 

Hi, maybe the lampholder have issues?

I tried directly connecting it to my ballast terminals. Still the same.

Could really be a weak ignitor. Some lamps, mainly the modern ones, require the ignitor to have really high voltage, but also exactly correct timing in respect to the mains voltage phase (they need to strike at or before the voltage peak, to allow the ballast to establish thick, high current discharge really just as the gas gets ionized by the ignitor).
And they may need an ignitor generating its pulse really each halfcycle of the mains, so it can build up the ionization required for the lamp to start before it decays (many lamps require the ignitor continuing with its burst of 2 pulses per mains cycle for a few seconds). Mainly some older, higher energy ignitors generate just a single pulse not motre than 4..5x per second, that is way too infrequent for generally all MHlamps.
And also check, whether your ignitor is really rated to generate sufficient voltage peaks. Mainly with HPS are intentionally used ignitors not delivering more than about 2.5kV, to reduce the risks of damaging the fixture (socket, wiring,...) when the lamp fails to ignite for some reason. These are not suitable for MHs.

Update- the lamps were tested with a higher voltage pulse, but still didn't work. Looks like corrosion got to the insides and damaged the wires.

Another update- I ran one of the lamps' bare arctube and it works! I don't know how long it will last though.