You need to try to draw some sort of schematics.Hmmm ... with a load the neutral to ground voltage is around 120V ... without a load the meter is reading 15V.
Assuming your load is functioning, there must be 120V between the other end of the load and the wire which you call "neutral" (otherwise the load wouldn't function). You say this is 120V between "neutral" and ground. This leaves us two possibilities:
1. There's 120+120V=240V on the other side of the load (relative to the ground). If there's a place which is 240V from ground, your house is totally miswired and one of the hot legs is connected to the ground. Easy to check. Measure between each of the legs and ground. If you get 240V/0V, your ground is wrong.
2. There's 120-120=0V on the other side of the load (relative to the ground). If that's true, the load is connected between ground and what you call "neutral", which actually means that it's not really neutral, but some hot wire of white color. When it gets energized, you get 120V. When not, some sort of device, such as dimmer or fancy 3-way switch pulls this wire to the ground. Easy to check too - look for dimmers and three way switches and measure conductivity between them and your "neutral".
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