Question: I have a rather concrete issue for those of you well versed in the chemical sciences:

The situation
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I know for a fact that most of the bottles I am using have been contaminated on the inside with vegetable oil during label removal. In retrospect, my situation could have been easily prevented, but in the mean time I do have hundreds of sub-optimal bottles that I badly want to use. I want to dissolve and remove the fat to make the bottles usable again. 

The questions
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1. Is fat dissolution possible while retaining the integrity of the glassware?
2. Which detergents or chemicals should i use, and what is their actual effect?

Answer: 
I would start with a mild dish washing soap with warm water, it usually gets rid of grease and oils. If you have a bottle brush, use it, if not shake the bottles well. Then rince the bottles well. If the glass bottles fit in your dishwasher, you can also give them a wash there first (glass only, not PET).

If this doesn't work, then I would look for a stronger product, but this should be enough.
I would suggest using a citric acid based cleaner to attempt to dissolve the fat. Leave it for a day or two and use a bottle brush to scrub the rest away