Which greenhouse gas has the most influence over global warming?
The annual amount of CO2 we emit from using carbon that was in relatively long-term sequestration (coal, natural gas, petroleum) is on the order of 40 GT. To put this in perspective: the amount of food humans consume over the same period of time is on the order of 4 GT. Our CO2 production is an order of magnitude larger than worldwide food consumption. And the problem with it is that it takes weathering to remove it from the atmosphere - meaning it can stay around for millennia, and we're very definitely the ones extracting it from the ground.

H2O only stays in the atmosphere as long as the temperature allows. This means that it won't be the driving factor. There is a slight positive feedback with more H2O leading to a warming so it can hold more H2O, but there's also a negative feedback of about the same size with cloud formation reflecting the sunlight back to space.

Ozone in the upper atmosphere is responsible for the warming at the Stratopause. It's the reason why we have our atmosphere divided into layers with the Troposphere getting cooler with height, the Stratosphere getting warmer with increased height, and the Mesosphere getting cooler again with height. The Ozone absorbs the very energetic solar radiation that would otherwise destroy the DNA in your skin and cause cancers, but as it's a triatomic molecule, it's also very good at absorbing longwave radiation. In this case, a hole in the ozone above the Antarctic may be allowing slightly more longwave radiation to escape - and repairing the hole so we humans can survive might also be trapping additional heat. https://climate.nasa.gov/faq/15/is-the-ozone-hole-causing-climate-change/

CH4 stays in the atmosphere on the order of a decade before chemically reacting with oxygen molecules to become CO2 and H2O - but while it's present, the effect is about two orders of magnitude greater than that of CO2. But since the methane hydrates have been stable, they're not culpable in the warming. Although there are large quantities in tundra and ocean shelves, there's little point in making it the talking factor for anything except scare tactics.

This page https://www.epa.gov/ghgemissions/overview-greenhouse-gases discusses the relative sizes emitted, but temper this with the measurements of these gases. CH4 us currently less than 2 ppmv and CO2 is over 400 ppmv, making it easily the biggest factor in our warming, and in fact, the warming from CO2 is what's causing the tundra to melt and the East Siberian Arctic Shelf (the largest on the planet) to warm and release its methane.

This is why we concentrate on CO2 (it being the largest factor and also the only one we seem to have much control over).

Hopefully this puts it into perspective, and you can do your yandex.com searches for more details.