Sweet probably was a poor choice of words on my part. By sweet, I just meant that it doesn't taste or smell like anything other than water. We have well water at home, so we're used to water that doesn't taste like city water.
What happens here, is that the well water goes into the tank and is fine for a couple days, after which it starts coming out of the faucets smelling pretty damn bad. Usually this is just in the lines, and it's fine after running it for a short time (although it still means the lines have an issue). Most recently, it's bad even coming out of the tanks (checked the tanks directly). There are no visible sludge in the tanks or anything like that.
My guess is that the water starts to allow stuff to grow either A) because it has stuff in it from the ground that likes to grow, or B) because it doesn't have anything in it to prevent stuff from growing, or C) a little of both of these.
I can take care of getting the system clean to start, but I'm not sure how to keep it that way since we're using well water and that by nature will be more difficult to keep clean when compared to city water.
We're not looking for perfection here, just not stinking and being safe for washing dishes is a good start.
What is actually wrong with the water ? You say it isn't sweet, do you just mean it has a bland dead taste, or do you actually mean it isn't as sweet (alkaline). The acidity of the water shouldn't change, so I would be surprised if it was becoming less sweet, what is more likely happening is that it is just becoming stagnant. The way you "bring it back to life" is by adding oxygen, sink water usually does that at the tap, the tap disperses the water as it comes out of the faucet, you end up with a glass full of water with bubbles in it. If you are used to drinking city water you are probably used to the taste of treatment chemicals in your water and well water just won't taste the same without them. One way you can test to see what is wrong with the water (in your opinion) is to boil some water and then let it cool over night, then try drinking it. If the taste of that water is the same thing you don't like about your tank water, the problem is that your water needs more oxygen to liven it up.