A Ph.D. is still useful for clinical work if you are willing to put in the time commitment it takes to attain it. That's because clinical physicists with Ph.D.'s have more upward mobility and will tend to get better salaries than their peers with masters degrees only. You can check out the AAPM website for some stats on medical physics jobs.
That being said, a Ph.D. certainly isn't necessary to get involved in clinical physics. However, keep in mind that while a Ph.D. is almost always funded by the department a masters degree will require you to take out some significant loans unless you happen to be independently wealthy.
There is little demand for physicists in nuclear medicine and diagnostic imaging. I don't know about health physics but it's probably a bit better. Radiation oncology has the most demand..
As far as responsibilities diagnostic imaging physicists typically work to keep machines up to standards by performing QA (quality assessment), contacting vendors when there's an issue and basically doing a whole lot of mundane maintenance tasks like calibrating the non-linearity corrections tables on a gamma camera. In nuclear medicine those responsibilities my be extended to calculating doses for nuclear medicine treatments such as I-131 ablation or the FDG dosages for PET scans. Because there isn't much to do in these areas there are very few positions that are 100% clinical in these areas. In universities you will typically find that diagnostic physicists are 40% clinical and 60% research and there is only one of them.
Medical health physicists jobs vary a bit more if I remember correctly. They can range from calculating the thickness of the walls necessary to block out a certain amount of radiation when facilities like radation therapy wings of hospitals are designed to measuring radiation levels around nuclear power plants to overseeing radiation workers and monitoring their doses by issuing personal dosimeters.
Medical physicists working in radiation therapy (clinical medical physicists) oversee treatment planning (which is typically done by dosimetrists), calibrate and commission LINACs, perform QA, possibly calibrate, monitor and issue dosimeters.