A thoracic fistula, such as a tracheo-oesophageal fistula, is best seen with a barium swallow. However it is generally performed with the patient prone, since the oesophagus is posterior to the trachea, and the barium needs to travel through the fistula. Great care must be taken to make sure the barium does not enter the lungs as well, since it can settle and set hard.
An abdominal GIT fistula would be best seen with a CT virtual colonoscopy or colonography. These are non-invasive tests that do not require contrast. The patient is required to drink a large amount of water to distend the bowel, but apart from that it is very similar to a normal CT abdomen scan. A single-contrast barium enema may also be a good test, but it is more invasive and more uncomfortable for the patient.
A uterine fistula can be demonstrated on ultrasound trans-vaginal scans, which I would expect to be the modality of choice. A CT scan would probably show it as well. The other option would be a hysterosalpinogram (HSG), which involves filling the uterus with contrast. This test is designed to show the uterine wall, specifically as a fertility test, but it is not common any more since it has been largely replaced by ultrasound.