The Setup

To achieve what you want, you'll simply have to wire all the light circuits in parallel off the common of the 3-way. Basically instead of a light on the common, you'll have light circuits. Something like this.

Following this scheme, each single pole switch will control the lights in a single area. While the whole circuit, is controlled by the 3-way switches. This way, if the 3-ways are OFF all the lights will be off. If the 3-ways are ON, the individual single pole switches will determine which lights are on.

The down side

While this configuration is possible, it may be confusing to any future owners of the home. This may also cause problems if the area is ever finished and actually divided into separate spaces, since a somebody could potentially be lost in the dark.

Code compliance

I'm not sure at this point whether or not this setup is code compliant, but a quick call to your local government should yield the answer. I will continue to review the National Electrical Code (NEC), to determine if there are any sections that would not allow a setup like this. If I find any restrictions, I will update this section of the answer.

_{If any others happen to know any codes that might apply here, please post the code section as a comment.}

That looks like a doorbell transformer. Those smaller wires should lead to your doorbell chime unit (assuming you have a doorbell). The junction box is there simply to provide power to the doorbell transformer.

From the picture it looks like you have 12/3 and 14/2 in that box, but it is difficult to tell. How confident are you the larger wires are larger than #12?

Figure out what breaker is supplying power to that circuit. As long as it is sized appropriately for the smallest conductors on the circuit, it will be fine. For example, if that is indeed a mix of #12 and #10 copper, your breaker must be 20A or smaller.

Also as a side note, NM cables entering that metal junction box need to be secured with a cable clamp. Any unused knockout holes need to be plugged. It looks like you've got a couple of code violations there at the top of your picture.