Essential oils are generally volatile in nature that give fragrance or smell to the product. It can be quantified by simple hydrodistillation using clevenger apparatus. Chemoprofile of oil can be assessed by using GCMS or HPLC.
You can extract oil by different solvents (hexane or chloroform: methanol, acetone) using soxhlet. and you can detect and identify by preparing FAME and analyze by GC-MS.