Basically, on nights designated as formal, men will be around 50/50 on tuxes and dark suits and ties. Ball gowns and highly formal wear for women is pretty much a thing of the past.
On casual nights, men wear slacks and a nice shirt. Women can actually do the same, or wear casual dresses, etc.
On informal nights, the men do the same as on casual nights, except add a sports jacket (tie OK but not required). Women "accesserize" up their casual dresses.
Radisson is actually a pretty casual line, and many of their cruises have no formal nights at all. So there is no reason to dress above what I've stated.