If the entire system is affected (and it sounds like it is) that would suggest a problem with one of the battery cables.
You can check whether it's the battery negative cable easily and without spending any money - if you have a set of jumper cables. Do it by creating a temporary redundant ground path to the battery from the engine.
Using just one cable of the jumper set (pos or neg), clamp one end to a good clean/unpainted spot on the engine. When you have that end clamped, connect the other end to the negative post of the battery. That's it. You now have - what amounts to - a new, extra negative battery cable installed alongside the normal cable.
If you notice a marked improvement in system voltage (e.g. the lights are brighter, the horn beeps and the radio plays, etc.) buy a real negative cable and install it.
If there is no improvement, you could try the same trick buy running one of the jumper cables from the battery positive down to the "B" terminal on the starter solenoid. Or you could just gamble and buy a new one (maybe $20) and hope for the best.
The only other thing that comes to mind is a shorted alternator that is pulling down your system voltage. Try disconnecting the 3 leads to the alternator - do it after the negative cable test but before the positive cable test. Not for any engineering reasons, but just because it's hard to do any work on the positive cable...and always do the easy stuff first.