Question is as the title suggests; what is the best thing to do with offerings once they’ve served their purpose. Do you burn them? Bury them? In the case of food, do you eat them?
Once the food have served it’s purpose you can just dispose of it as any food you wouldn’t eat. Wine/water I throw out in the earth sometimes, but food I do not eat as I leave it for 3 days usually, nor do I throw it out unless I lay it out at the crossroads.
This is a very common question, so I highly recommend you try using the search function to find an answer before making a post.
Offerings are traditionally disposed of through the elements. Libations can be poured out upon the earth, and food can be buried, or thrown into a body of water.
Never eat an offering unless the spirit asks you to.
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The first offering I ever made to King Paimon was one of my favorite lambic beers.
I didn’t know what I was doing with food offerings yet and I was looking at his glass thinking - I’ll just drink it.
I got a stern warning from him to never do that again. He let me off the hook because I had done out of ignorance.
But he insisted I never ever do that with any other entity/deity.
But as you say there can be an exception.
King Asmoday let’s me eat or drink any of his food offerings. 
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I have always thought the sensory experience is more pertinent to just leaving an offering strewn across an altar? Ie eat the promised offering or drink it in the daemons presence to feed the experience unto it. Or not give an offering at all as its not really a given to do so.