Pretty much every drain in my house is running slow or backs-up. Is there a central problem with the drainage or should I tackle each situation idependantly?

Do you have a septic tank? It may need to be pumped out, drains will generally drain slowly and then maybe a day or 2 later start to back up, and that means your tank is FULL.

If it's not a septic tank problem, then I am guessing that it is a central problem, since it's all of them, but I wouldn't know where to start.

Good luck with your plumbing troubles!

If the entire house has a problem it is likely the main drain going out to the city sewer or septic. Do not start taking each drain apart, you'lll waste your time and energy. There is usually a clean out in the verticle stack in the basement. If you open it and there is not standing water the clog is prior to the stack further back in the house plumbing. If there is stand water in the stack the clog is between you and the city sewer riser and you should rod from this location. A 3" cutter would be a good start with the snake. Let us know what you find and maybe we can be of further assistance.