Which are bicycle-politicized groups or advocate groups?
I don't know of any truly worldwide organizations of that type, and doubt any are out there. I believe you'll have an easier time finding a local organization. I believe a local organization is also going to be more effective at achieving the goals you mention.

Bicycle advocacy of getting better infrastructure (roads, paths, lanes, etc) will have to be focused on the government agencies responsible for constructing and maintaining that infrastructure. Laws about bicycles are an important aspect, too. Cities, counties, states, provinces and countries are responsible for roads and laws, not international/worldwide organizations.

For example, I live in California, in a city about 50 miles from San Francisco. There's a local county-wide organization (bicycle coalition) that works with the county-wide government and the governments of many of the cities inside the county. That county bicycle coalition is affiliated with an organization that covers the whole San Francisco bay area and deals primarily with programs that cover that whole area. Then there is a California-wide coalition. And there are several US-wide national organizations, with one (the League of American Bicyclists) that they all seem to work with somewhat.

There are also organizations that advocate for non-automobile ("alternative") transportation, for pedestrians, for public transportation, for less fossil-fuel usage, etc. Some of those are focused specifically on their particular issue, but many include some amount of bicycle advocacy, too.


League of American Bicyclists (nation-wide US organization) has list of international and US nationwide organizations on their website.
Ask at your LBS like @ChrisW says above. The bike shop is likely to be a member of at least one advocacy organization, since better bicycle infrastructure will help them sell more bikes.
Find out about local public meetings related to planning for cycling infrastructure, show up and look for other bicyclists there (does your city have a council/board that meets regularly and publicly that you can find out the agenda for and check when there's transportation issues on the agenda? Maybe a committee or board or something that plans the city's transportation?).
Get some other dedicated bicycle-people together, start your own, and figure out who in your local government to talk to in order to improve the bicycle infrastructure in your own area.