Ah, the bare wires in the attic... you're not the first old house owner to see that. I found nearly sixteen feet with absolutely no insulation at all, next to a couple of mouse skeletons. Others have found the problem when tracking down the smell of a dead squirrel. It seems wire insulation is irresistibly tasty, and low occupancy areas like attics are where rodents can feast on it at their leisure.
Unfortunately, it's extremely difficult to completely exclude mice from an old house. The rule of thumb is "if a dime can fit through it, a mouse can fit through it". It can take many years to rodent-proof a house, and in the meantime, it might burn to the ground!
So I strongly recommend you replace all the horizontal wire runs in the attic with metallic sheathed cable. It's commonly called "greenfield" around here, but typically sold as type AC, MC, BX, or armored cable; I don't know why it has so many names. The steel jacketed type is literally mouse proof, and even the softer aluminum coated stuff seems to be enough to discourage them.. they could chew through it if they really wanted to, but I've never seen it happen.
(My local electrical code actually requires use of metallic sheathed cable anywhere that rodents are expected to be encountered, although this is usually interpreted by inspectors as meaning agricultural buildings and sheds.)
I also recommend you have the current carrying capacity of the circuit you're using for your toaster oven checked. It's not terribly uncommon for people to stupidly replace fuses or circuit breakers with larger ones, which can also lead to your house burning down. When the voltage is dropping like that, it can be an indication that the wiring is literally melting - it's almost certainly overheating, although it might be just at a junction point rather than over the entire wire run.
Whenever I add, repair or replace wiring in an old house I always use greenfield. The additional cost is not high compared to labor costs - and never having to replace it due to mouse or squirrel damage is much cheaper in the long run.