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: 
What not use a commercial brewing steriliser/cleaner like VWP? Soak in a solution made with very hot water overnight. One might find that all that is needed thereafter is a rinse with fresh water and drain dry. If necessary a scrub with a bottle brush should complete the job.
Specifically, 
1) It should be easy to get rid of the fat/oil without compromising the glassware
2) A VPW is a good cleaning/degreasing agent that loosens and solvates fats and oils and it also is a source of chlorine that will sterilise the bottle at the same time.

However it may not be that the oily residue is causing the lack of head retention. That can be due to a myriad of reasons but hopefully using some VWP will indicate if the bottle contaminants are the cause.
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