The first steps of essential oil testing usually begins with sensory evaluation, since this saves wasting precious time and money on more expensive analytical procedures and can identify inferior oils quickly. The viscosity, color, clarity and odor of an essential oil can help to identify a poor quality oil right at the outset - provided you know precisely what to look for.
An odor test can also help to determine if an oil is really what it purports to be, since certain adulterants can be identified in this way. Some essential oils such as Lavender are available from several geographical locations, and a trained nose will be able to detect if a so called 'French' Lavender is in fact from another, less desirable (or less expensive) origin.
If an essential oil sample passes all of the sensory tests, the next stage is to test the physical parameters of the essential oil by means of measuring the Specific Gravity, Optical Rotation and Refractive Index.
If an oil successfully passes the first two stages it is then tested using Gas Chromatography/Mass Spectrometry (GC/MS). GC-FID is the best one for these purpose.
Every individual component of the essential oil can be identified by the time at which the peak elutes on the trace. The data produced can then be compared to an established 'profile' or 'fingerprint' for that particular essential oil to finally determine the purity of the oil.
As you are working on the antifungal activity, I would suggest you to perform following tests also (Microbiological evaluation):
Total Plate Count
Total Coliforms
Bacteria
Salmonella
Yeast and Mold
Hereby I also attach a paper for your ready reference.
The Bureau of Indian Standards has published physico-chemical standards for different Indian essential oils. The booklet on each essential oil briefly describes the method by which the value is determined. You may visit their site for more information.