This is an ongoing major class-action case, officially Lindsay Cooper, et al v. Tokyo Electric Power Company, et al. in the 9th US Federal Circuit.
The OP does not reasonably describe the health problems of the sailors in the lawsuit, which are allegedly caused by the radiation. Instead, according to their website:
The lawsuit includes claims for illnesses such as Leukemia, ulcers, gall bladder removals, brain cancer, brain tumors, testicular cancer, dysfunctional uterine bleeding, thyroid illnesses, stomach ailments and a host of other complaints unusual in such young adults.
Yesterday (4/5/2016), according to 9th Circ. Agrees To Speed Up Sailors' $1B Fukushima Suit, a judge granted a motion by the sailors to speed up the case.
The sailors had argued:
The balance of appellee service members are experiencing various stages of cancer and other ailments associated with radiation exposure .... With each passing month, appellees’ conditions are worsening and many will most probably die before seeing a resolution to their lawsuit. For others, a prompt resolution will bring them the funds required to obtain specialized and advanced medical treatments that could, if employed early enough, save their lives.
On the other hand TEPCO pointed to US Department of Defense statements that radiation doses were too low to cause the problems.
Specifically, there is the Final Report to the Congressional Defense Committees in Response to
the Joint Explanatory Statement Accompanying the Department of Defense
Appropriations Act, 2014, page 90, “Radiation Exposure” which concludes:
There is no objective evidence that the RONALD REAGAN sailors experienced
radiation exposures during OT that would result in an increase in the expected number of
radiogenic diseases over time. The estimated radiation doses for all individuals in the OT
registry (OTR), including RONALD REAGAN sailors, were very small and well below levels
associated with the occurrence of adverse medical conditions.
The US Department of Defense has created Operation Tomodachi Registry (OTR):
The OTR includes nearly 75,000 DOD-affiliated individuals who were on or near the mainland of Japan during the period from March 12, 2011 to May 11, 2011, along with their corresponding whole-body and thyroid radiation doses. Over 58,000 individuals were associated with one of 13 shore-based locations, which included DOD military installations and major cities where the majority of the DOD-affiliated population worked or lived. Nearly 17,000 individuals were associated with U.S. Navy fleet-based locations, which included the 25 U.S. Navy ships (and aircrew) in the area during this period.