Overcast is not the problem. You're getting radiation energy from the sun, right through the clouds. Ideally, all your stuff should run on a common type of battery. If that isn't possible, make sure you have adaptors. Which are a pain, depending on what's at stake. You can 'daisy chain' a few of your items. My Schosce (sic) can charge from a wall socket, and charge the phone at the same time. Since what you need, as you describe the conditions, is a solar system costing upwards of $1,000. It might cost less, and be more efficient, to have devices with USB2-3, USB mini, and USB micro sockets. Unless you carry a travel battery charger, your AAA, AA, C and D cannot be charged directly off your solar. IF the device has a USB connector, you can wisely charge the batteries inside the device, and not need a separate battery charger. Maybe, and I say maybe as in, "Maybe not." your net-top battery can be the system battery, if you have extra USB connectons on the net-top.
If you really have to have a lot of power, look at gel-cell motorcycle batteries. But every time you leave town, you'll have to lug a ten pound battery with you.