I have an old house with old wiring. I have no colors to go by.
By electrical code (not sure how old this code is, but I think very old) if there are 2 wires for a circuit the one with any type of marking is the neutral or negative wire. For instance, it is common for a cord to have 1 smooth wire and 1 ribbed wire (there are raised grooves that go the length of the wire), the ribbed wire is the neutral. Or in outlets the larger plug hole is the neutral. Testing the continuity to ground is the best method, but make sure to turn the breaker off before you test it, as you might break your meter if you test continuity of a hot circuit.
consider a rewire , sounds overdue .
It should have continuity (low ohms) when tested against the general mass of earth.
You can test it with a voltmeter to something that is grounded like a metal water pipe. One wire will have 115 to 120 volts to ground (the hot wire) and the other will be 0 volts (the neutral). You may need one long piece of wire to reach from the water line to where you are testing the wires. Another way is to use a non-contact voltage tester. It will glow when it is next to the hot wire but not when it is next to the neutral. You can get them at a building supply or hardware store for about $10. I prefer the first method because it is more sure but the second one is easier. There is no positive or negative on AC wiring.
How To Identify Neutral Wire