Formal Politics refers to the operation of a constitutional system of government and publicly defined institutions and procedures. Political parties, public policy or discussions about war and foreign affairs would fall under the category of Formal Politics. Many people view formal politics as something outside of themselves, but that can still affect their daily lives.
Informal Politics is understood as forming alliances, exercising power and protecting and advancing particular ideas or goals. Generally, this includes anything affecting one's daily life, such as the way an office or household is managed, or how one person or group exercises influence over another. Informal Politics is typically understood as everyday politics, hence the idea that "politics is everywhere".
A political organization is any entity that is involved in the political process. Political organization including political institution, political parties, political groups- e.g. advocacy groups, Interest groups etc. .
Political organizations are engaged in political activities aimed at achieving clearly defined political goals, which improve political system, benefit the interests of their members- e.g., members organizing, campaign, labor unions, etc.
While parties are one type of political organization that enlisted with election authority & engage in some or all of those activities, they are distinct in that they typically focus on supporting candidates for public office, winning elections and forming government.