Interesting thing about a liquid fueled forge is that the fuel is usually burned in a separate area. Look up ursutz burner (it is spelled that way); an ursutz is a box shaped device that, once heated, easily burns liquid fuels that are hard to ignite. If I wanted to run it off of only gasoline or diesel/kerosine then a separate burner is not needed, but it doesn't hurt if designed well.
The design is quite simple, a forced air device shoots air into a box. The box shape stirrs up turbulence in the air. Oil/fuel is dripped into the air stream, it is vaporized by the moving air. Mine actually uses a separate vaporizer but it works without one

The fuel/air are mixed thoroughly in the box, which if preheated (torched or fire built inside box) lets the fuel burn. It is shot out an opening and into a forge.
Design considerations:
The box should be lined with refractory, if not the metal is likely to be useless after only a few firings.
If not preheated the oil will not light on its own. I solved this simply, run it off kerosine diesel or gas for a few mins then dump the oil into the fuel tank.
The burner can be separated from the forge body, so one burner can be used to operate a variety of heating devices given that its output is varied.
When waste veggie oil is burned completely (hot enough fire) is leaves fewer impurities and bi-products behind than propane!!!! I cannot verify if this is true...just told to me by an alternative fuel scientist.
So lets recap...
My burner is separate from the forge. Runs off gasoline for a few mins before the wvo is poured into the tank. Tank has a needle valve on it and is attatched to a compressor in a vaporizer set-up. This vaporizer is positioned to face right down into the burner. The forge itself can operate on its side for standard knife forging, or upright for salt baths and cruicible melting.
Oh and keep in mind, I have no idea what I am doing

Knives are new to me, fire is not