Disgust, sicken, nauseate are comparable when meaning to arouse an extreme distaste in.
Disgust implies a stomach that is revolted by food offered or taken; in its extended use it implies sensibilities which are revolted by something seen, heard, or otherwise known that creates strong repugnance or aversion.
Sicken usually implies not only the exciting of distaste but of actual physical distress (as faintness or a turning of the stomach); often, however, it is used merely as a more emphatic word for disgust, or it may suggest a disgust born of weariness or exhaustion.
Nauseate carries a stronger implication than disgust or sicken of loathsomeness (as to the taste, sight, or mind), and often suggests retching or vomiting.