In any partitioning of material between phases, like oil and water, there will be some of each phase left in the other phase. So you have to determine how much material is important to be able to measure in each phase. Do you need to concentrate residual oil from the water phase? The other open question is whether the oil of interest is volatile enough to be analyzed by GC?

To analyze the water solution after separating oil from an oil-water mixture, you can use several methods, including GC/HPLC. Here are some steps you can follow:

Sample Preparation: You will need to prepare your water sample for analysis. Depending on the method you choose, the sample preparation method may vary. For GC analysis, you will need to extract the compounds of interest from the water sample. You can use an organic solvent such as hexane to extract the compounds. For HPLC analysis, you can directly inject the water sample into the HPLC system.

Chromatographic Separation: After preparing your sample, you will need to separate the compounds of interest using a chromatography technique. For GC analysis, you can use gas chromatography to separate the compounds based on their volatility. For HPLC analysis, you can use high-performance liquid chromatography to separate the compounds based on their polarity.

Detection: Once the compounds are separated, you can detect them using a suitable detector. For GC analysis, you can use a flame ionization detector (FID) or a mass spectrometer (MS) to detect the separated compounds. For HPLC analysis, you can use a UV-vis detector or a mass spectrometer to detect the separated compounds.

Data Analysis: Finally, you will need to analyze the data obtained from the detector to determine the composition of the water sample. You can compare the chromatographic peaks obtained from the sample with those obtained from a reference sample to identify the compounds present in the water sample.

Maybe you could retain the residual organic phase in water by eluting your sample through a solid-phase extractor with low polarity and then you can extract the retained organics by eluting them in an organic solvent or a mix of solvents.

After this step, you can inject your sample into a GC-MS to identify and quantify your analytes.

You can even spike your sample with an internal standard before the extraction to help smooth the quantification process.

However, I would advise looking for an already-tested and convenient method available in the literature for the kind of sample that you have. You would probably find the kind of solid-phase extractor and solvents, as well as the previous chromatographic conditions and chromatographic column that you should use to solve your problem.