To keep it brief, soaking can be used to aid in two different aspects of the oil. Yield and Abundance of known oudh compounds.
The Yield,
soaking alters the wood morphology, causing the cell wall to break down easier for the oils to escape. If we were to imagine the oil pockets inside the wood as little sacks, the normal distillation process will force out the oils from this sack, with parts still remaining in the sack. When the actual sack breaks apart all the oil leaks out. This assist the yield.
When every bit of oil from the wood is distilled out, this also adds to the quality of the oil, increasing the abundance of the compounds that give oudh it's oudhyness. Such oils smell and measure in gcms to have more favourable compounds.
The graph below produced by Veronica Alexandar Jok et al, at the university of technology in Shah Alam Malaysia, demonstrates that the yield increases with the right amount of soaking. The vast majority of the data places that duration of 'perfect' soaking for yield at 14 days.
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Abundance of Known Compounds,
Abundance is a term utilised in measuring how many of a specific compound exists in the oil. When soaking goes beyond 21 days, the known compounds that contribute to the oudhyness decreases but other compounds increase. Oudh oils have been known to have between 30-100+ different compounds in them, depending on how long they have been soaked, the temperatures that they have been cooked in, and the length of the cook. for example according to Jutarut Pornpunyapat et al, changing the temperature from 80 C - 120 C nearly doubles the number of positive contributing compounds in A.Crassna samples and also the quantity of each compound is increased significantly. Please see the attached tables.
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As such it can clearly be seen that soaking can be used to increase the yield, manipulate the abundance % of compounds i.e longer soak reduces the abundance % ultimately changing the scent profile.