I don't know the extent of purification you want, but the filtration then mixing of pure water followed by separation is helpful. Give enough time to separation
First filtration to separate solids present in the oil after washing with water to remove small amounts of salt. After treat with sodium methoxide in amounts suitable for obtaining biodiesel.
waste cooking oil contains various waste particles. first separate the larger particle by sieving through the micron size holes and then pour luke warm water to remove the salts and then separate it.
The links of the articles may be useful for your need.
The first, even being used for crude vegetable oil, can be applied to the residual oil. The second shows an example of biodiesel production using rapidly purified waste oil.